# File kernel/src/modelingTools/SecondOrderDS.hpp#

Go to the source code of this file

class SecondOrderDS : public DynamicalSystem
#include <SecondOrderDS.hpp>

Second Order non linear dynamical systems - $$M(q,z) \dot v = F(v, q, t, z) + p$$.

This class defines and computes a generic ndof-dimensional second order Non Linear Dynamical System of the form :

$\begin{split} M(q,z) \dot v = F(v, q, t, z) + p \\ \dot q = G(q,v) \end{split}$

where

• $$q \in R^{ndof}$$ is the set of the coordinates,

• $$\dot q =v \in R^{ndof}$$ the velocity,

• $$\ddot q = \dot v \in R^{ndof}$$ the acceleration, i. e. the second time derivative of the generalized coordinates.

• $$p \in R^{ndof}$$ the reaction forces due to the Non Smooth Interaction.

• $$M(q) \in R^{ndof \times ndof}$$ is the inertia term (access : mass() method).

• $$F( \dot q , q , t) \in R^{ndof}$$ are the forces (access forces() method).

• $$z \in R^{zSize}$$ is a vector of arbitrary algebraic variables, some sort of discrete state.

q[i] is the derivative number i of q. Thus: q[0]= $$q$$, global coordinates, q[1]= $$\dot q$$, velocity, q[2]= $$\ddot q$$, acceleration.

The following operators (and their jacobians) can be plugged, in the usual way (see User Guide, ‘User-defined plugins’)

If required (e.g. for Event-Driven like simulation), formulation as a first-order system is also available, and writes:

• $$n= 2 ndof$$

• $$x = \left[\begin{array}{c}q \\ \dot q\end{array}\right]$$

• rhs given by:

$\begin{split} \dot x = \left[\begin{array}{c} \dot q\\ \ddot q = M^{-1}(q)\left[F(v, q , t, z) + p \right]\\ \end{array}\right] \end{split}$

• jacobian of the rhs, with respect to x

$\begin{split} \nabla_{x}rhs(x,t) = \left[\begin{array}{cc} 0 & I \\ \nabla_{q}(M^{-1}(q)F(v, q , t, z)) & \nabla_{\dot q}(M^{-1}(q)F(v, q , t, z)) \\ \end{array}\right] \end{split}$
with the input due to the non smooth law:

$\begin{split} \left[\begin{array}{c} 0 \\ p \end{array}\right] \end{split}$

In that case, use the following methods:

Subclassed by LagrangianDS, NewtonEulerDS

Public Functions

inline virtual ~SecondOrderDS()

destructor

inline SP::SiconosVector p(unsigned int level = 2) const

get p

Parameters:

level – unsigned int, required level for p, default = 2

Returns:

pointer on a SiconosVector

inline SP::SiconosMatrix mass() const

Returns:

SP::SiconosMatrix

inline SP::SimpleMatrix inverseMass() const

get (pointer) inverse or LU-factorization of the mass, used for LU-forward-backward computation

Returns:

pointer SP::SimpleMatrix

inline void setMassPtr(SP::SimpleMatrix newPtr)

set mass to pointer newPtr

Parameters:

newPtr – a plugged matrix SP

inline virtual void setRhs(const SiconosVector &newValue) override

set the value of the right-hand side, $$\dot x$$

Parameters:

newValueSiconosVector

inline virtual void setRhsPtr(SP::SiconosVector newPtr) override

set right-hand side, $$\dot x$$ (pointer link)

Parameters:

newPtr – SP::SiconosVector

virtual void computeForces(double time, SP::SiconosVector q, SP::SiconosVector velocity) = 0

Compute $$F(v,q,t,z)$$.

Parameters:
• time – the current time

• q – SP::SiconosVector: pointers on q

• velocity – SP::SiconosVector: pointers on velocity

virtual void computeJacobianqForces(double time) = 0

Compute $$\nabla_qF(v,q,t,z)$$ for current $$q,v$$ Default function to compute forces.

Parameters:

time – the current time

virtual void computeJacobianvForces(double time) = 0

Compute $$\nabla_{\dot q}F(v,q,t,z)$$ for current $$q,v$$.

Parameters:

time – the current time

inline virtual unsigned int dimension() const override

return the number of degrees of freedom of the system

Returns:

an unsigned int.

virtual SP::SiconosVector q() const = 0

generalized coordinates of the system (vector of size dimension())

Returns:

pointer on a SiconosVector

virtual void setQ(const SiconosVector &newValue) = 0

set value of generalized coordinates vector (copy)

Parameters:

newValue

virtual void setQPtr(SP::SiconosVector newPtr) = 0

set value of generalized coordinates vector (pointer link)

Parameters:

newPtr

inline SP::SiconosVector q0() const

Returns:

pointer on a SiconosVector

virtual void setQ0(const SiconosVector &newValue) = 0

set initial state (copy)

Parameters:

newValue

virtual void setQ0Ptr(SP::SiconosVector newPtr) = 0

Parameters:

newPtr

virtual SP::SiconosVector velocity() const = 0

Returns:

pointer on a SiconosVector

virtual void setVelocity(const SiconosVector &newValue) = 0

set velocity vector (copy)

Parameters:

newValue

virtual void setVelocityPtr(SP::SiconosVector newPtr) = 0

Parameters:

newPtr

virtual SP::SiconosVector velocity0() const = 0

get initial velocity (pointer)

Returns:

pointer on a SiconosVector

virtual void setVelocity0(const SiconosVector &newValue) = 0

set initial velocity (copy)

Parameters:

newValue

virtual void setVelocity0Ptr(SP::SiconosVector newPtr) = 0

Parameters:

newPtr

virtual SP::SiconosVector acceleration() const = 0

Returns:

pointer on a SiconosVector

virtual SP::SiconosVector forces() const = 0

get $$F(v,q,t,z)$$ (pointer link)

Returns:

pointer on a SiconosVector

virtual SP::SiconosMatrix jacobianqForces() const = 0
Returns:

$$\nabla_qF(v,q,t,z)$$ (pointer link)

virtual SP::SiconosMatrix jacobianvForces() const = 0

get $$\nabla_{\dot q}F(v,q,t,z)$$ (pointer link)

Returns:

pointer on a SiconosMatrix

virtual const SiconosMemory &qMemory() = 0

get all the values of the state vector q stored in memory.

note: not const due to SchatzmanPaoliOSI::initializeWorkVectorsForDS

Returns:

a memory

virtual const SiconosMemory &velocityMemory() = 0

get all the values of the state vector velocity stored in memory.

note: not const due to SchatzmanPaoliOSI::initializeWorkVectorsForDS

Returns:

a memory

virtual const SiconosMemory &forcesMemory() = 0

get forces in memory buff

Returns:

pointer on a SiconosMemory

virtual void initMemory(unsigned int size) override = 0

initialize the SiconosMemory objects with a positive size.

Parameters:

size – the size of the SiconosMemory. must be >= 0

virtual void computeMass() = 0

default function to compute the mass

virtual void computeMass(SP::SiconosVector position) = 0

function to compute the mass

Parameters:

position – value used to evaluate the mass matrix

virtual void setBoundaryConditions(SP::BoundaryCondition newbd)

set Boundary Conditions

Parameters:

newbd – BoundaryConditions

inline SP::BoundaryCondition boundaryConditions()

get Boundary Conditions

Returns:

SP::BoundaryCondition pointer on a BoundaryConditions

inline void setReactionToBoundaryConditions(SP::SiconosVector newrbd)

set Reaction to Boundary Conditions

Parameters:

newrbd – BoundaryConditions pointer

inline SP::SiconosVector reactionToBoundaryConditions()

get Reaction to Boundary Conditions

Returns:

pointer on a BoundaryConditions

virtual void init_inverse_mass() = 0

Allocate memory for the lu factorization of the mass of the system.

Useful for some integrators with system inversion involving the mass

virtual void update_inverse_mass() = 0

Update the content of the lu factorization of the mass of the system, if required.

virtual void init_forces() = 0

Allocate memory for forces and its jacobian.

ACCEPT_STD_VISITORS()#

Protected Functions

ACCEPT_SERIALIZATION(SecondOrderDS)#
inline SecondOrderDS()#
inline SecondOrderDS(unsigned int dimension, unsigned int ndof)#

minimal constructor, from state dimension result in $$\dot x = r$$

Parameters:

dimension – size of the system (n)

Protected Attributes

unsigned int _ndof#

number of degrees of freedom of the system

SP::SiconosMatrix _mass#

mass of the system

bool _hasConstantMass = false#

true if the mass matrix is constant

SP::SimpleMatrix _inverseMass#

inverse or factorization of the mass of the system

std::vector<SP::SiconosVector> _p#

“Reaction”, generalized forces or imuplses due to the non smooth law The index corresponds to the kinematic level of the corresponding constraints.

It mainly depends on what the simulation part want to store, but some rules have to be followed. For instance :

• for the constraints at the acceleration level, _p[2] stores the reaction forces,

• for the constraints at the veocity level, _p[1] stores the (discrete) reaction impulse

• for the constraints at the position level, _p[0] stores the multiplier for a constraint in position

SP::SiconosVector _q0#

Initial position.

VectorOfMemories _pMemory#

memory of previous generalized forces due to constraints

SP::BoundaryCondition _boundaryConditions#

Boundary condition applied to a dynamical system.

SP::SiconosVector _reactionToBoundaryConditions#

Reaction to an applied boundary condition.