File kernel/src/modelingTools/LagrangianR.hpp

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class LagrangianR : public Relation

#include <LagrangianR.hpp>

Lagrangian Non Linear Relation (generic interface)

This class is an interface for specific Lagrangian Relations used for Lagrangian dynamical systems.

• \( y = h(t,q,\dot q,\ldots) \) describes the constraint (the relation)

• The Jacobian of the constraints with respect to the coodinates \( q \) i.e. \( \nabla^T_q h(t,q,\dot q,\ldots) \) , is accessed with jachq().

This Jacobian is mainly used for Newton linearization and to compute the time-derivative of the constraint,

\( y = h(q,\ldots) \) that is \( \dot y (t) = \nabla^T_q h(t,q,\dot q,\ldots) (q) \dot q +\ldots \)

This object can also store more general linearized part of the gap function. If \( y=h(q) \) models a gap function, then the time derivative can be generically written as

\( \dot y (t) = H(q,\ldots) \dot q +\ldots. \) The matrix \( H(q,\ldots) \) can also be accessed using jachq().

• The Jacobian of the constraints with respect to the generalized velocities \( \dot q \)

i.e. \( \nabla^\top_{\dot q} h(t,q,\dot q,\ldots) \) is accessed using jachqDot().

• The time-derivative of Jacobian of the constraints with respect to the generalized coordinates \( q \)

i.e. \( \frac{d}{dt} \nabla^\top_{q} h(t,q,\dot q,\ldots). \) , is accessed using dotJachq().

This value is useful to compute the second-order time&#8212;derivative of the constraints with respect to time.

All these operators can be defined with user-defined plugins.

Subclassed by LagrangianCompliantLinearTIR, LagrangianCompliantR, LagrangianLinearTIR, LagrangianRheonomousR, LagrangianScleronomousR

Public Types

enum LagrangianRDS

Values:

enumerator z

enumerator q0

enumerator q1

enumerator q2

enumerator p0

enumerator p1

enumerator p2

enumerator DSlinkSize

Public Functions

virtual ~LagrangianR() noexcept = default

destructor

inline virtual void initialize(Interaction &inter) override

initialize the relation (check sizes, memory allocation …)

Parameters:

inter – the interaction using this relation

inline SP::SimpleMatrix jachq() const

get a pointer on matrix Jach[index]

Returns:

a pointer on a SimpleMatrix

inline SP::SimpleMatrix jachqDot() const

inline SP::SimpleMatrix dotJachq() const

inline SP::SimpleMatrix jachlambda() const

inline void setJachqPtr(SP::SimpleMatrix newPtr)

set Jach[index] to pointer newPtr (pointer link)

Parameters:

newPtr – the new matrix

inline virtual SP::SimpleMatrix C() const override

inline virtual SP::SimpleMatrix H() const override

virtual void display() const override

main relation members display

Protected Functions

ACCEPT_SERIALIZATION(LagrangianR)

inline LagrangianR(RELATION::SUBTYPES lagType)

basic constructor

Parameters:

lagType – the sub-type of the relation

virtual void _zeroPlugin() override

To initialize all the plugin functions with nullptr.

Protected Attributes

SP::SimpleMatrix _jachlambda = {nullptr}

Jacobian matrices of \( y = h(t,q,\dot q,\ldots) \)

SP::SimpleMatrix _jachq = {nullptr}

The Jacobian of the constraints with respect to the generalized coodinates \( q \) i.e.

\( \nabla^\top_q h(t,q,\dot q,\ldots) \)

SP::SimpleMatrix _jachqDot = {nullptr}

The Jacobian of the constraints with respect to the generalized velocities \( \dot q \) i.e.

\( \nabla^\top_{\dot q} h(t,q,\dot q,\ldots) \)

SP::SimpleMatrix _dotjachq = {nullptr}

The time-derivative of Jacobian of the constraints with respect to the generalized coordinates \( q \) i.e.

\( \frac{d}{dt} \nabla^\top_{ q} h(t,q,\dot q,\ldots). \) This value is useful to compute the second-order time&#8212;derivative of the constraints with respect to time.

SP::PluggedObject _pluginJachq = {nullptr}