Drake
BeadOnAWire< T > Class Template Reference

Dynamical system of a point (unit) mass constrained to lie on a wire. More...

#include <drake/examples/bead_on_a_wire/bead_on_a_wire.h>

Inheritance diagram for BeadOnAWire< T >:
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Collaboration diagram for BeadOnAWire< T >:
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## Public Types

enum  CoordinateType { kMinimalCoordinates, kAbsoluteCoordinates }
The type of coordinate representation to use for kinematics and dynamics. More...

typedef Eigen::AutoDiffScalar< drake::Vector1dAScalar
AutoDiff scalar used for constraint function automatic differentiation. More...

typedef Eigen::AutoDiffScalar< Eigen::Matrix< AScalar, 1, 1 > > ArcLength
AutoDiff scalar used for computing the second derivative of the constraint function using automatic differentiation. More...

## Public Member Functions

Constructs the object using either minimal or absolute coordinates (the latter uses the method of Lagrange Multipliers to compute the time derivatives). More...

void set_gravitational_acceleration (double g)
Sets the acceleration (with respect to the positive y-axis) due to gravity (i.e., this number should generally be negative). More...

double get_gravitational_acceleration () const
Gets the acceleration (with respect to the positive y-axis) due to gravity (i.e., this number should generally be negative). More...

void reset_wire_parameter_functions (std::function< Eigen::Matrix< ArcLength, 3, 1 >(const ArcLength &)> f, std::function< ArcLength(const Eigen::Matrix< ArcLength, 3, 1 > &)> inv_f)
Allows the user to reset the wire parameter function and its inverse (which points to helix_function and inverse_helix_function by default. More...

Public Member Functions inherited from LeafSystem< T >
~LeafSystem () override

std::unique_ptr< CompositeEventCollection< T > > AllocateCompositeEventCollection () const final
Allocates a CompositeEventCollection object for this system. More...

std::unique_ptr< Context< T > > AllocateContext () const override
Allocates a context, initialized with the correct numbers of concrete input ports and state variables for this System. More...

void SetDefaultState (const Context< T > &context, State< T > *state) const override
Default implementation: sets all continuous and discrete state variables to zero. More...

virtual void SetDefaultParameters (const LeafContext< T > &context, Parameters< T > *parameters) const
Default implementation: sets all numeric parameters to the model vector given to DeclareNumericParameter, or else if no model was provided sets the numeric parameter to one. More...

void SetDefaults (Context< T > *context) const final

std::unique_ptr< SystemOutput< T > > AllocateOutput (const Context< T > &context) const final
Returns a container that can hold the values of all of this System's output ports. More...

std::unique_ptr< ContinuousState< T > > AllocateTimeDerivatives () const override
Returns the AllocateContinuousState value, which must not be nullptr. More...

std::unique_ptr< DiscreteValues< T > > AllocateDiscreteVariables () const override
Returns the AllocateDiscreteState value, which must not be nullptr. More...

std::multimap< int, intGetDirectFeedthroughs () const final
Reports all direct feedthroughs from input ports to output ports. More...

LeafSystem (const LeafSystem &)=delete

LeafSystemoperator= (const LeafSystem &)=delete

LeafSystem (LeafSystem &&)=delete

LeafSystemoperator= (LeafSystem &&)=delete

Public Member Functions inherited from System< T >
virtual ~System ()

void GetWitnessFunctions (const Context< T > &context, std::vector< const WitnessFunction< T > * > *w) const
Gets the witness functions active at the beginning of a continuous time interval. More...

EvaluateWitness (const Context< T > &context, const WitnessFunction< T > &witness_func) const
Evaluates a witness function at the given context. More...

std::string GetSystemIdString () const
Returns a string suitable for identifying this particular System in error messages, when it is a subsystem of a larger Diagram. More...

System (const System &)=delete

Systemoperator= (const System &)=delete

System (System &&)=delete

Systemoperator= (System &&)=delete

std::unique_ptr< BasicVector< T > > AllocateInputVector (const InputPortDescriptor< T > &descriptor) const
Given a port descriptor, allocates the vector storage. More...

std::unique_ptr< AbstractValueAllocateInputAbstract (const InputPortDescriptor< T > &descriptor) const
Given a port descriptor, allocates the abstract storage. More...

std::unique_ptr< Context< T > > CreateDefaultContext () const
This convenience method allocates a context using AllocateContext() and sets its default values using SetDefaults(). More...

void AllocateFreestandingInputs (Context< T > *context) const
For each input port, allocates a freestanding input of the concrete type that this System requires, and binds it to the port, disconnecting any prior input. More...

bool HasAnyDirectFeedthrough () const
Returns true if any of the inputs to the system might be directly fed through to any of its outputs and false otherwise. More...

bool HasDirectFeedthrough (int output_port) const
Returns true if there might be direct-feedthrough from any input port to the given output_port, and false otherwise. More...

bool HasDirectFeedthrough (int input_port, int output_port) const
Returns true if there might be direct-feedthrough from the given input_port to the given output_port, and false otherwise. More...

void Publish (const Context< T > &context, const EventCollection< PublishEvent< T >> &events) const
This method is the public entry point for dispatching all publish event handlers. More...

void Publish (const Context< T > &context) const
Forces a publish on the system, given a context. More...

const T & EvalConservativePower (const Context< T > &context) const
Returns a reference to the cached value of the conservative power. More...

const T & EvalNonConservativePower (const Context< T > &context) const
Returns a reference to the cached value of the non-conservative power. More...

template<template< typename > class Vec = BasicVector>
const Vec< T > * EvalVectorInput (const Context< T > &context, int port_index) const
Causes the vector-valued input port with the given port_index to become up-to-date, delegating to our parent Diagram if necessary. More...

Eigen::VectorBlock< const VectorX< T > > EvalEigenVectorInput (const Context< T > &context, int port_index) const
Causes the vector-valued input port with the given port_index to become up-to-date, delegating to our parent Diagram if necessary. More...

const AbstractValueEvalAbstractInput (const Context< T > &context, int port_index) const
Causes the abstract-valued input port with the given port_index to become up-to-date, delegating to our parent Diagram if necessary. More...

template<typename V >
const V * EvalInputValue (const Context< T > &context, int port_index) const
Causes the abstract-valued input port with the given port_index to become up-to-date, delegating to our parent Diagram if necessary. More...

int get_num_constraint_equations (const Context< T > &context) const
Gets the number of constraint equations for this system using the given context (useful in case the number of constraints is dependent upon the current state (as might be the case with a system modeled using piecewise differential algebraic equations). More...

Eigen::VectorXd EvalConstraintEquations (const Context< T > &context) const
Evaluates the constraint equations for the system at the generalized coordinates and generalized velocity specified by the context. More...

Eigen::VectorXd EvalConstraintEquationsDot (const Context< T > &context) const
Computes the time derivative of each constraint equation, evaluated at the generalized coordinates and generalized velocity specified by the context. More...

Eigen::VectorXd CalcVelocityChangeFromConstraintImpulses (const Context< T > &context, const Eigen::MatrixXd &J, const Eigen::VectorXd &lambda) const
Computes the change in velocity from applying the given constraint forces to the system at the given context. More...

double CalcConstraintErrorNorm (const Context< T > &context, const Eigen::VectorXd &error) const
Computes the norm on constraint error (used as a metric for comparing errors between the outputs of algebraic equations applied to two different state variable instances). More...

void CalcTimeDerivatives (const Context< T > &context, ContinuousState< T > *derivatives) const
Calculates the time derivatives xcdot of the continuous state xc. More...

void CalcDiscreteVariableUpdates (const Context< T > &context, const EventCollection< DiscreteUpdateEvent< T >> &events, DiscreteValues< T > *discrete_state) const
This method is the public entry point for dispatching all discrete variable update event handlers. More...

void CalcDiscreteVariableUpdates (const Context< T > &context, DiscreteValues< T > *discrete_state) const
This method forces a discrete update on the system given a context, and the updated discrete state is stored in discrete_state. More...

void CalcUnrestrictedUpdate (const Context< T > &context, const EventCollection< UnrestrictedUpdateEvent< T >> &events, State< T > *state) const
This method is the public entry point for dispatching all unrestricted update event handlers. More...

void CalcUnrestrictedUpdate (const Context< T > &context, State< T > *state) const
This method forces an unrestricted update on the system given a context, and the updated state is stored in discrete_state. More...

CalcNextUpdateTime (const Context< T > &context, CompositeEventCollection< T > *events) const
This method is called by a Simulator during its calculation of the size of the next continuous step to attempt. More...

void GetPerStepEvents (const Context< T > &context, CompositeEventCollection< T > *events) const
This method is called by Simulator::Initialize() to gather all update and publish events that are to be handled in StepTo() at the point before Simulator integrates continuous state. More...

void CalcOutput (const Context< T > &context, SystemOutput< T > *outputs) const
Utility method that computes for every output port i the value y(i) that should result from the current contents of the given Context. More...

CalcPotentialEnergy (const Context< T > &context) const
Calculates and returns the potential energy current stored in the configuration provided in context. More...

CalcKineticEnergy (const Context< T > &context) const
Calculates and returns the kinetic energy currently present in the motion provided in the given Context. More...

CalcConservativePower (const Context< T > &context) const
Calculates and returns the rate at which mechanical energy is being converted from potential energy to kinetic energy by this system in the given Context. More...

CalcNonConservativePower (const Context< T > &context) const
Calculates and returns the rate at which mechanical energy is being generated (positive) or dissipated (negative) other than by conversion between potential and kinetic energy (in the given Context). More...

void MapVelocityToQDot (const Context< T > &context, const VectorBase< T > &generalized_velocity, VectorBase< T > *qdot) const
Transforms a given generalized velocity v to the time derivative qdot of the generalized configuration q taken from the supplied Context. More...

void MapVelocityToQDot (const Context< T > &context, const Eigen::Ref< const VectorX< T >> &generalized_velocity, VectorBase< T > *qdot) const
Transforms the given generalized velocity to the time derivative of generalized configuration. More...

void MapQDotToVelocity (const Context< T > &context, const VectorBase< T > &qdot, VectorBase< T > *generalized_velocity) const
Transforms the time derivative qdot of the generalized configuration q to generalized velocities v. More...

void MapQDotToVelocity (const Context< T > &context, const Eigen::Ref< const VectorX< T >> &qdot, VectorBase< T > *generalized_velocity) const
Transforms the given time derivative qdot of generalized configuration q to generalized velocity v. More...

void set_name (const std::string &name)
Sets the name of the system. More...

std::string get_name () const
Returns the name last supplied to set_name(), or empty if set_name() was never called. More...

std::string GetMemoryObjectName () const
Returns a name for this System based on a stringification of its type name and memory address. More...

void GetPath (std::stringstream *output) const
Writes the full path of this System in the tree of Systems to output. More...

std::string GetPath () const

int get_num_input_ports () const
Returns the number of input ports of the system. More...

int get_num_output_ports () const
Returns the number of output ports of the system. More...

const InputPortDescriptor< T > & get_input_port (int port_index) const
Returns the descriptor of the input port at index port_index. More...

const OutputPort< T > & get_output_port (int port_index) const
Returns the output port at index port_index. More...

int get_num_constraints () const
Returns the number of constraints specified for the system. More...

const SystemConstraint< T > & get_constraint (SystemConstraintIndex constraint_index) const
Returns the constraint at index constraint_index. More...

int get_num_total_inputs () const
Returns the total dimension of all of the input ports (as if they were muxed). More...

int get_num_total_outputs () const
Returns the total dimension of all of the output ports (as if they were muxed). More...

void CheckValidOutput (const SystemOutput< T > *output) const
Checks that output is consistent with the number and size of output ports declared by the system. More...

template<typename T1 = T>
void CheckValidContext (const Context< T1 > &context) const
Checks that context is consistent for this System template. More...

VectorX< T > CopyContinuousStateVector (const Context< T > &context) const
Returns a copy of the continuous state vector xc into an Eigen vector. More...

void set_parent (const detail::InputPortEvaluatorInterface< T > *parent)
Declares that parent is the immediately enclosing Diagram. More...

std::string GetGraphvizString () const
Returns a Graphviz string describing this System. More...

int64_t GetGraphvizId () const
Returns an opaque integer that uniquely identifies this system in the Graphviz output. More...

void FixInputPortsFrom (const System< double > &other_system, const Context< double > &other_context, Context< T > *target_context) const
Fixes all of the input ports in target_context to their current values in other_context, as evaluated by other_system. More...

std::unique_ptr< System< AutoDiffXd > > ToAutoDiffXd () const
Creates a deep copy of this System, transmogrified to use the autodiff scalar type, with a dynamic-sized vector of partial derivatives. More...

std::unique_ptr< System< AutoDiffXd > > ToAutoDiffXdMaybe () const
Creates a deep copy of this system exactly like ToAutoDiffXd(), but returns nullptr if this System does not support autodiff, instead of throwing an exception. More...

std::unique_ptr< System< symbolic::Expression > > ToSymbolic () const
Creates a deep copy of this System, transmogrified to use the symbolic scalar type. More...

std::unique_ptr< System< symbolic::Expression > > ToSymbolicMaybe () const
Creates a deep copy of this system exactly like ToSymbolic(), but returns nullptr if this System does not support symbolic, instead of throwing an exception. More...

## Static Public Member Functions

static Eigen::Matrix< ArcLength, 3, 1 > helix_function (const ArcLength &s)
Example wire parametric function for the bead on a wire example. More...

static ArcLength inverse_helix_function (const Vector3< ArcLength > &v)
Inverse parametric function for the bead on a wire system that uses the helix parametric example function. More...

static Eigen::Vector3d get_pfunction_output (const Eigen::Matrix< ArcLength, 3, 1 > &m)
Gets the output from the parametric function in Vector3d form. More...

static Eigen::Vector3d get_pfunction_first_derivative (const Eigen::Matrix< ArcLength, 3, 1 > &m)
Gets the first derivative from the parametric function, in Vector3d form, using the output from that parametric function. More...

static Eigen::Vector3d get_pfunction_second_derivative (const Eigen::Matrix< ArcLength, 3, 1 > &m)
Gets the second derivative from the parametric function, in Vector3d form, using the output from that parametric function. More...

static double get_inv_pfunction_output (const ArcLength &m)
Gets the output from the inverse parametric function as a double, using the output from that inverse parametric function. More...

static double get_inv_pfunction_first_derivative (const ArcLength &m)
Gets the first derivative from the inverse parametric function as a double, using the output from that inverse parametric function. More...

static double get_inv_pfunction_second_derivative (const ArcLength &m)
Gets the second derivative from the inverse parametric function as a double, using the output from that inverse parametric function. More...

Static Public Member Functions inherited from System< T >
template<template< typename > class S = ::drake::systems::System>
static std::unique_ptr< S< AutoDiffXd > > ToAutoDiffXd (const S< T > &from)
Creates a deep copy of from, transmogrified to use the autodiff scalar type, with a dynamic-sized vector of partial derivatives. More...

template<template< typename > class S = ::drake::systems::System>
static std::unique_ptr< S< symbolic::Expression > > ToSymbolic (const S< T > &from)
Creates a deep copy of from, transmogrified to use the symbolic scalar type. More...

## Protected Member Functions

void CopyStateOut (const systems::Context< T > &context, systems::BasicVector< T > *output) const

void DoCalcTimeDerivatives (const systems::Context< T > &context, systems::ContinuousState< T > *derivatives) const override

void SetDefaultState (const systems::Context< T > &context, systems::State< T > *state) const override
Sets the default state for the bead-on-a-wire system to s = 0, ds/dt = 0 for the bead represented in minimal coordinates; for the bead represented in absolute coordinates, the default state is set to f(0), ds/dt(0)⋅0 = 0. More...

int do_get_num_constraint_equations (const systems::Context< T > &context) const override
Gets the number of constraint equations used for dynamics. More...

Eigen::VectorXd DoEvalConstraintEquations (const systems::Context< T > &context) const override
Evaluates the constraint equations for a bead represented in absolute coordinates (no constraint equations are used for a bead represented in minimal coordinates). More...

Eigen::VectorXd DoEvalConstraintEquationsDot (const systems::Context< T > &context) const override
Computes the time derivative of the constraint equations, evaluated at the current generalized coordinates and generalized velocity. More...

Eigen::VectorXd DoCalcVelocityChangeFromConstraintImpulses (const systems::Context< T > &context, const Eigen::MatrixXd &J, const Eigen::VectorXd &lambda) const override
Computes the change in generalized velocity from applying constraint impulses lambda. More...

Protected Member Functions inherited from LeafSystem< T >
LeafSystem ()
Default constructor that declares no inputs, outputs, state, parameters, events, nor scalar-type conversion support (AutoDiff, etc.). More...

LeafSystem (SystemScalarConverter converter)
Constructor that declares no inputs, outputs, state, parameters, or events, but allows subclasses to declare scalar-type conversion support (AutoDiff, etc.). More...

System< AutoDiffXd > * DoToAutoDiffXd () const override
NVI implementation of ToAutoDiffXdMaybe. More...

System< symbolic::Expression > * DoToSymbolic () const override
NVI implementation of ToSymbolicMaybe. More...

virtual std::unique_ptr< LeafContext< T > > DoMakeContext () const
Provides a new instance of the leaf context for this system. More...

DoEvaluateWitness (const Context< T > &context, const WitnessFunction< T > &witness_func) const final
Derived classes will implement this method to evaluate a witness function at the given context. More...

void AddTriggeredWitnessFunctionToCompositeEventCollection (const WitnessFunction< T > &witness_func, CompositeEventCollection< T > *events) const final
Add witness_func to events. More...

void DoCalcNextUpdateTime (const Context< T > &context, CompositeEventCollection< T > *events, T *time) const override
Computes the next update time based on the configured periodic events, for scalar types that are arithmetic, or aborts for scalar types that are not arithmetic. More...

BasicVector< T > * DoAllocateInputVector (const InputPortDescriptor< T > &descriptor) const override
Allocates a vector that is suitable as an input value for descriptor. More...

AbstractValueDoAllocateInputAbstract (const InputPortDescriptor< T > &descriptor) const override
Allocates an AbstractValue suitable as an input value for descriptor. More...

void GetGraphvizFragment (std::stringstream *dot) const override
Emits a graphviz fragment for this System. More...

void GetGraphvizInputPortToken (const InputPortDescriptor< T > &port, std::stringstream *dot) const final
Appends a fragment to the dot stream identifying the graphviz node representing port. More...

void GetGraphvizOutputPortToken (const OutputPort< T > &port, std::stringstream *dot) const final
Appends a fragment to the dot stream identifying the graphviz node representing port. More...

virtual std::unique_ptr< ContinuousState< T > > AllocateContinuousState () const
Returns a ContinuousState used to implement both CreateDefaultContext and AllocateTimeDerivatives. More...

virtual std::unique_ptr< DiscreteValues< T > > AllocateDiscreteState () const
Reserves the discrete state as required by CreateDefaultContext. More...

virtual std::unique_ptr< AbstractValuesAllocateAbstractState () const
Reserves the abstract state as required by CreateDefaultContext. More...

virtual std::unique_ptr< Parameters< T > > AllocateParameters () const
Reserves the parameters as required by CreateDefaultContext. More...

virtual optional< boolDoHasDirectFeedthrough (int input_port, int output_port) const
Returns true if there is direct-feedthrough from the given input_port to the given output_port, false if there is not direct-feedthrough, or nullopt if unknown (in which case SystemSymbolicInspector will attempt to measure the feedthrough using symbolic form). More...

int DeclareNumericParameter (const BasicVector< T > &model_vector)
Declares a numeric parameter using the given model_vector. More...

template<template< typename > class U = BasicVector>
const U< T > & GetNumericParameter (const Context< T > &context, int index) const
Extracts the numeric parameters of type U from the context at index. More...

template<template< typename > class U = BasicVector>
U< T > * GetMutableNumericParameter (Context< T > *context, int index) const
Extracts the numeric parameters of type U from the context at index. More...

template<typename EventType >
void DeclarePeriodicEvent (double period_sec, double offset_sec)
Declares that this System has a simple, fixed-period event specified with no custom callback function, and its attribute field contains an Event<T>::PeriodicAttribute constructed from the specified period_sec and offset_sec. More...

template<typename EventType >
void DeclarePeriodicEvent (double period_sec, double offset_sec, const EventType &event)
Declares that this System has a simple, fixed-period event specified by event. More...

void DeclarePeriodicDiscreteUpdate (double period_sec, double offset_sec=0)
Declares a periodic discrete update event with period = period_sec and offset = offset_sec. More...

void DeclarePeriodicUnrestrictedUpdate (double period_sec, double offset_sec=0)
Declares a periodic unrestricted update event with period = period_sec and offset = offset_sec. More...

void DeclarePeriodicPublish (double period_sec, double offset_sec=0)
Declares a periodic publish event with period = period_sec and offset = offset_sec. More...

template<typename EventType >
void DeclarePerStepEvent (const EventType &event)
Declares a per-step event using event, which is deep copied (the copy is maintained by this). More...

void DeclareContinuousState (int num_state_variables)
Declares that this System should reserve continuous state with num_state_variables state variables, which have no second-order structure. More...

void DeclareContinuousState (int num_q, int num_v, int num_z)
Declares that this System should reserve continuous state with num_q generalized positions, num_v generalized velocities, and num_z miscellaneous state variables. More...

void DeclareContinuousState (const BasicVector< T > &model_vector)
Declares that this System should reserve continuous state with model_vector.size() miscellaneous state variables, stored in a vector Cloned from model_vector. More...

void DeclareContinuousState (const BasicVector< T > &model_vector, int num_q, int num_v, int num_z)
Declares that this System should reserve continuous state with num_q generalized positions, num_v generalized velocities, and num_z miscellaneous state variables, stored in a vector Cloned from model_vector. More...

void DeclareContinuousState (std::unique_ptr< BasicVector< T >> model_vector, int num_q, int num_v, int num_z)
Declares that this System should reserve continuous state with num_q generalized positions, num_v generalized velocities, and num_z miscellaneous state variables, stored in the a vector Cloned from model_vector. More...

void DeclareDiscreteState (int num_state_variables)
Declares that this System should reserve discrete state with num_state_variables state variables. More...

int DeclareAbstractState (std::unique_ptr< AbstractValue > abstract_state)
Declares an abstract state. More...

template<class MySystem >
SystemConstraintIndex DeclareEqualityConstraint (void(MySystem::*calc)(const Context< T > &, VectorX< T > *) const, int count, const std::string &description)
Declares a system constraint of the form f(context) = 0 by specifying a member function to use to calculate the (VectorX) constraint value with a signature: More...

SystemConstraintIndex DeclareEqualityConstraint (typename SystemConstraint< T >::CalcCallback calc, int count, const std::string &description)
Declares a system constraint of the form f(context) = 0 by specifying a std::function to use to calculate the (Vector) constraint value with a signature: More...

template<class MySystem >
SystemConstraintIndex DeclareInequalityConstraint (void(MySystem::*calc)(const Context< T > &, VectorX< T > *) const, int count, const std::string &description)
Declares a system constraint of the form f(context) ≥ 0 by specifying a member function to use to calculate the (VectorX) constraint value with a signature: More...

SystemConstraintIndex DeclareInequalityConstraint (typename SystemConstraint< T >::CalcCallback calc, int count, const std::string &description)
Declares a system constraint of the form f(context) ≥ 0 by specifying a std::function to use to calculate the (Vector) constraint value with a signature: More...

virtual void DoPublish (const Context< T > &context, const std::vector< const PublishEvent< T > * > &events) const
Derived-class event handler for all simultaneous publish events in events. More...

virtual void DoCalcDiscreteVariableUpdates (const Context< T > &context, const std::vector< const DiscreteUpdateEvent< T > * > &events, DiscreteValues< T > *discrete_state) const
Derived-class event handler for all simultaneous discrete update events. More...

virtual void DoCalcUnrestrictedUpdate (const Context< T > &context, const std::vector< const UnrestrictedUpdateEvent< T > * > &events, State< T > *state) const
Derived-class event handler for all simultaneous unrestricted update events. More...

const InputPortDescriptor< T > & DeclareVectorInputPort (const BasicVector< T > &model_vector)
Declares a vector-valued input port using the given model_vector. More...

const InputPortDescriptor< T > & DeclareAbstractInputPort (const AbstractValue &model_value)
Declares an abstract-valued input port using the given model_value. More...

template<class MySystem , typename BasicVectorSubtype >
const OutputPort< T > & DeclareVectorOutputPort (const BasicVectorSubtype &model_vector, void(MySystem::*calc)(const Context< T > &, BasicVectorSubtype *) const)
Declares a vector-valued output port by specifying (1) a model vector of type BasicVectorSubtype derived from BasicVector and initialized to the correct size and desired initial value, and (2) a calculator function that is a class member function (method) with signature: More...

template<class MySystem , typename BasicVectorSubtype >
const OutputPort< T > & DeclareVectorOutputPort (void(MySystem::*calc)(const Context< T > &, BasicVectorSubtype *) const)
Declares a vector-valued output port by specifying only a calculator function that is a class member function (method) with signature: More...

const OutputPort< T > & DeclareVectorOutputPort (const BasicVector< T > &model_vector, typename LeafOutputPort< T >::CalcVectorCallback vector_calc_function)
(Advanced) Declares a vector-valued output port using the given model_vector and a function for calculating the port's value at runtime. More...

template<class MySystem , typename OutputType >
const OutputPort< T > & DeclareAbstractOutputPort (const OutputType &model_value, void(MySystem::*calc)(const Context< T > &, OutputType *) const)
Declares an abstract-valued output port by specifying a model value of concrete type OutputType and a calculator function that is a class member function (method) with signature: More...

template<class MySystem , typename OutputType >
const OutputPort< T > & DeclareAbstractOutputPort (void(MySystem::*calc)(const Context< T > &, OutputType *) const)
Declares an abstract-valued output port by specifying only a calculator function that is a class member function (method) with signature: More...

template<class MySystem , typename OutputType >
const OutputPort< T > & DeclareAbstractOutputPort (OutputType(MySystem::*make)(const Context< T > &) const, void(MySystem::*calc)(const Context< T > &, OutputType *) const)
Declares an abstract-valued output port by specifying member functions to use both for the allocator and calculator. More...

template<class MySystem , typename OutputType >
const OutputPort< T > & DeclareAbstractOutputPort (OutputType(MySystem::*make)() const, void(MySystem::*calc)(const Context< T > &, OutputType *) const)
Declares an abstract-valued output port by specifying member functions to use both for the allocator and calculator. More...

const OutputPort< T > & DeclareAbstractOutputPort (typename LeafOutputPort< T >::AllocCallback alloc_function, typename LeafOutputPort< T >::CalcCallback calc_function)
(Advanced) Declares an abstract-valued output port using the given allocator and calculator functions provided in their most generic forms. More...

Protected Member Functions inherited from System< T >
virtual void DoGetWitnessFunctions (const Context< T > &, std::vector< const WitnessFunction< T > * > *) const
Derived classes can override this method to provide witness functions active at the beginning of a continuous time interval. More...

SystemConstraintIndex AddConstraint (std::unique_ptr< SystemConstraint< T >> constraint)
Adds an already-created constraint to the list of constraints for this System. More...

const EventCollection< PublishEvent< T > > & get_forced_publish_events () const

const EventCollection< DiscreteUpdateEvent< T > > & get_forced_discrete_update_events () const

const EventCollection< UnrestrictedUpdateEvent< T > > & get_forced_unrestricted_update_events () const

void set_forced_publish_events (std::unique_ptr< EventCollection< PublishEvent< T >>> forced)

void set_forced_discrete_update_events (std::unique_ptr< EventCollection< DiscreteUpdateEvent< T >>> forced)

void set_forced_unrestricted_update_events (std::unique_ptr< EventCollection< UnrestrictedUpdateEvent< T >>> forced)

System ()
Constructs an empty System base class object. More...

const InputPortDescriptor< T > & DeclareInputPort (PortDataType type, int size)
Adds a port with the specified type and size to the input topology. More...

const InputPortDescriptor< T > & DeclareAbstractInputPort ()
Adds an abstract-valued port to the input topology. More...

void CreateOutputPort (std::unique_ptr< OutputPort< T >> port)
Adds an already-created output port to this System. More...

virtual void DoCalcTimeDerivatives (const Context< T > &context, ContinuousState< T > *derivatives) const
Override this if you have any continuous state variables xc in your concrete System to calculate their time derivatives. More...

virtual T DoCalcPotentialEnergy (const Context< T > &context) const
Override this method for physical systems to calculate the potential energy currently stored in the configuration provided in the given Context. More...

virtual T DoCalcKineticEnergy (const Context< T > &context) const
Override this method for physical systems to calculate the kinetic energy currently present in the motion provided in the given Context. More...

virtual T DoCalcConservativePower (const Context< T > &context) const
Override this method to return the rate at which mechanical energy is being converted from potential energy to kinetic energy by this system in the given Context. More...

virtual T DoCalcNonConservativePower (const Context< T > &context) const
Override this method to return the rate at which mechanical energy is being generated (positive) or dissipated (negative) other than by conversion between potential and kinetic energy (in the given Context). More...

virtual void DoMapQDotToVelocity (const Context< T > &context, const Eigen::Ref< const VectorX< T >> &qdot, VectorBase< T > *generalized_velocity) const
Provides the substantive implementation of MapQDotToVelocity(). More...

virtual void DoMapVelocityToQDot (const Context< T > &context, const Eigen::Ref< const VectorX< T >> &generalized_velocity, VectorBase< T > *qdot) const
Provides the substantive implementation of MapVelocityToQDot(). More...

virtual int do_get_num_constraint_equations (const Context< T > &context) const
Gets the number of constraint equations for this system from the given context. More...

virtual Eigen::VectorXd DoEvalConstraintEquations (const Context< T > &context) const
Evaluates the constraint equations for the system at the generalized coordinates and generalized velocity specified by the context. More...

virtual Eigen::VectorXd DoEvalConstraintEquationsDot (const Context< T > &context) const
Computes the time derivative of each constraint equation, evaluated at the generalized coordinates and generalized velocity specified by the context. More...

virtual Eigen::VectorXd DoCalcVelocityChangeFromConstraintImpulses (const Context< T > &context, const Eigen::MatrixXd &J, const Eigen::VectorXd &lambda) const
Computes the change in velocity from applying the given constraint forces to the system at the given context. More...

virtual double DoCalcConstraintErrorNorm (const Context< T > &context, const Eigen::VectorXd &error) const
Computes the norm of the constraint error. More...

Eigen::VectorBlock< VectorX< T > > GetMutableOutputVector (SystemOutput< T > *output, int port_index) const
Returns a mutable Eigen expression for a vector valued output port with index port_index in this system. More...

void EvalInputPort (const Context< T > &context, int port_index) const
Causes an InputPortValue in the context to become up-to-date, delegating to the parent Diagram if necessary. More...

## Detailed Description

### template<typename T> class drake::examples::bead_on_a_wire::BeadOnAWire< T >

Dynamical system of a point (unit) mass constrained to lie on a wire.

The system is currently frictionless. The equation for the wire can be provided parametrically by the user. Dynamics equations can be computed in both minimal coordinates or absolute coordinates (with Lagrange Multipliers).

The presence of readily available solutions coupled with the potential for highly irregular geometric constraints (which can be viewed as complex contact constraints), can make this a challenging problem to simulate.

The dynamic equations for the bead in minimal coordinates comes from Lagrangian Dynamics of the "second kind": forming the Lagrangian and using the Euler-Lagrange equation. The potential energy (V) of the bead with respect to the parametric function f(s) : ℝ → ℝ³ is:

-f₃(s)⋅ag


where ag is the magnitude (i.e., non-negative value) of the acceleration due to gravity. The velocity of the bead is df/ds⋅ṡ, and the kinetic energy of the bead (T) is therefore 1/2⋅(df/ds⋅ṡ)².

The Lagrangian is then defined as:

ℒ = T - V = 1/2⋅(df/ds)²⋅ṡ² + f₃(s)⋅ag


And Lagrangian Dynamics specifies that the dynamics for the system are defined by:

∂ℒ/∂s - d/dt ∂ℒ/∂ṡ = τ̇⋅


where τ is the generalized force on the system. Thus:

df(s)/ds⋅ṡ²⋅d²f/ds² + (df(s)/ds)₃⋅ag - (df/ds)²⋅dṡ/dt = τ


The dynamic equations for the bead in absolute coordinates comes from the Lagrangian Dynamics of the "first kind" (i.e., by formulating the problem as an Index-3 DAE):

d²x/dt² = fg + fext + Jᵀλ
g(x) = 0


where x is the three dimensional position of the bead, fg is a three dimensional gravitational acceleration vector, fext is a three dimensional vector of "external" (user applied) forces acting on the bead, and J ≡ ∂g/∂x is the Jacobian matrix of the positional constraints (computed with respect to the bead location). We define g(x) : ℝ³ → ℝ³ as the following function:

g(x) = f(f⁻¹(x)) - x


where f⁻¹ : ℝ³ → ℝ maps points in Cartesian space to wire parameters (this class expects that this inverse function may be ill-defined). g(x) = 0 will only be satisfied if x corresponds to a point on the wire.

This class uses Drake's -inl.h pattern. When seeing linker errors from this class, please refer to http://drake.mit.edu/cxx_inl.html.

Template Parameters
 T The vector element type, which must be a valid Eigen scalar.

Instantiated templates for the following scalar types T are provided:

• double

They are already available to link against in the library implementation.

Inputs: One input (generalized external force) for the bead on a wire simulated in minimal coordinates, three inputs (three dimensional external force applied to the center of mass) for the bead on a wire simulated in absolute coordinates.

States: Two state variables (arc length of the bead along the wire and the velocity of the bead along the wire) for the bead simulated in minimal coordinates; 3D position (state indices 0,1, and 2), and 3D linear velocity (state indices 3, 4, and 5) in units of m and m/s, respectively, for the bead simulated in absolute coordinates.

Outputs: same as state.

## Member Typedef Documentation

 typedef Eigen::AutoDiffScalar > ArcLength

AutoDiff scalar used for computing the second derivative of the constraint function using automatic differentiation.

The constraint function maps from an arc length (s) to a point in three-dimensional Cartesian space. This type represents the input variable s and- on return from that constraint function- would hold the second derivative of the constraint function computed with respect to s.

 typedef Eigen::AutoDiffScalar AScalar

AutoDiff scalar used for constraint function automatic differentiation.

The constraint function maps from an arc length (s) to a point in three-dimensional Cartesian space. This type represents the input variable s and- on return from that constraint function- would hold the first derivative of the constraint function computed with respect to s.

## Member Enumeration Documentation

 enum CoordinateType

The type of coordinate representation to use for kinematics and dynamics.

Enumerator
kMinimalCoordinates

Coordinate representation will be wire parameter.

kAbsoluteCoordinates

Coordinate representation will be the bead location (in 3D).

## Constructor & Destructor Documentation

 BeadOnAWire ( CoordinateType type )
explicit

Constructs the object using either minimal or absolute coordinates (the latter uses the method of Lagrange Multipliers to compute the time derivatives).

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## Member Function Documentation

 void CopyStateOut ( const systems::Context< T > & context, systems::BasicVector< T > * output ) const
protected

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 int do_get_num_constraint_equations ( const systems::Context< T > & context ) const
overrideprotected

Gets the number of constraint equations used for dynamics.

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 void DoCalcTimeDerivatives ( const systems::Context< T > & context, systems::ContinuousState< T > * derivatives ) const
overrideprotected

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 Eigen::VectorXd DoCalcVelocityChangeFromConstraintImpulses ( const systems::Context< T > & context, const Eigen::MatrixXd & J, const Eigen::VectorXd & lambda ) const
overrideprotected

Computes the change in generalized velocity from applying constraint impulses lambda.

Parameters
 context The current state of the system. lambda The vector of constraint forces.
Returns
a n dimensional vector, where n is the dimension of the quasi-coordinates.

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 Eigen::VectorXd DoEvalConstraintEquations ( const systems::Context< T > & context ) const
overrideprotected

Evaluates the constraint equations for a bead represented in absolute coordinates (no constraint equations are used for a bead represented in minimal coordinates).

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 Eigen::VectorXd DoEvalConstraintEquationsDot ( const systems::Context< T > & context ) const
overrideprotected

Computes the time derivative of the constraint equations, evaluated at the current generalized coordinates and generalized velocity.

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 double get_gravitational_acceleration ( ) const
inline

Gets the acceleration (with respect to the positive y-axis) due to gravity (i.e., this number should generally be negative).

 double get_inv_pfunction_first_derivative ( const ArcLength & m )
static

Gets the first derivative from the inverse parametric function as a double, using the output from that inverse parametric function.

Parameters
 m the output from the inverse parametric wire function.

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 double get_inv_pfunction_output ( const ArcLength & m )
static

Gets the output from the inverse parametric function as a double, using the output from that inverse parametric function.

Parameters
 m the output from the inverse parametric wire function.

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 double get_inv_pfunction_second_derivative ( const ArcLength & m )
static

Gets the second derivative from the inverse parametric function as a double, using the output from that inverse parametric function.

Parameters
 m the output from the inverse parametric wire function.

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 Eigen::Vector3d get_pfunction_first_derivative ( const Eigen::Matrix< ArcLength, 3, 1 > & m )
static

Gets the first derivative from the parametric function, in Vector3d form, using the output from that parametric function.

Parameters
 m the output from the parametric wire function.

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 Eigen::Vector3d get_pfunction_output ( const Eigen::Matrix< ArcLength, 3, 1 > & m )
static

Gets the output from the parametric function in Vector3d form.

Parameters
 m the output from the parametric wire function.

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 Eigen::Vector3d get_pfunction_second_derivative ( const Eigen::Matrix< ArcLength, 3, 1 > & m )
static

Gets the second derivative from the parametric function, in Vector3d form, using the output from that parametric function.

Parameters
 m the output from the parametric wire function.

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 Eigen::Matrix< typename BeadOnAWire< T >::ArcLength, 3, 1 > helix_function ( const ArcLength & s )
static

Example wire parametric function for the bead on a wire example.

The exact function definition is:

       | cos(s) |
f(s) = | sin(s) |
| s      |


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 BeadOnAWire< T >::ArcLength inverse_helix_function ( const Vector3< ArcLength > & v )
static

Inverse parametric function for the bead on a wire system that uses the helix parametric example function.

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 void reset_wire_parameter_functions ( std::function< Eigen::Matrix< ArcLength, 3, 1 >(const ArcLength &)> f, std::function< ArcLength(const Eigen::Matrix< ArcLength, 3, 1 > &)> inv_f )
inline

Allows the user to reset the wire parameter function and its inverse (which points to helix_function and inverse_helix_function by default.

Parameters
 f The pointer to a function that takes a wire parameter (scalar s) as input and outputs a point in 3D as output. inv_f The pointer to a function that takes a point in 3D as input and outputs a floating point scalar as output.
Exceptions
 std::logic_error if f or inv_f is a nullptr (the functions must always be set).

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 void set_gravitational_acceleration ( double g )
inline

Sets the acceleration (with respect to the positive y-axis) due to gravity (i.e., this number should generally be negative).

 void SetDefaultState ( const systems::Context< T > & context, systems::State< T > * state ) const
overrideprotected

Sets the default state for the bead-on-a-wire system to s = 0, ds/dt = 0 for the bead represented in minimal coordinates; for the bead represented in absolute coordinates, the default state is set to f(0), ds/dt(0)⋅0 = 0.

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The documentation for this class was generated from the following files: