Ode equation of 2nd order of the form \(M(x,v).a = F(x, v)\) with \((x0, v0)\) for initial conditions and a set of boundary conditions. More...

#include <OdeEquation.h>

Inheritance diagram for SurgSim::Math::OdeEquation:

Public Member Functions
virtual	~OdeEquation ()
	Virtual destructor.

const std::shared_ptr< OdeState >	getInitialState () const
	Retrieves the ode initial conditions \((x0, v0)\) (i.e the initial state) More...

virtual Matrix	applyCompliance (const OdeState &state, const Matrix &b)=0
	Calculate the product \(C.b\) where \(C\) is the compliance matrix with boundary conditions applied. More...

virtual void	updateFMDK (const OdeState &state, int options)
	Update the OdeEquation (and support data) based on the given state. More...

const Vector &	getF () const

const SparseMatrix &	getM () const

const SparseMatrix &	getD () const

const SparseMatrix &	getK () const

bool	hasF () const

bool	hasM () const

bool	hasK () const

bool	hasD () const

Protected Member Functions
virtual void	computeF (const OdeState &state)=0
	Evaluation of the RHS function \(f(x, v)\) for a given state. More...

virtual void	computeM (const OdeState &state)=0
	Evaluation of the LHS matrix \(M(x,v)\) for a given state. More...

virtual void	computeD (const OdeState &state)=0
	Evaluation of \(D = -\frac{\partial f}{\partial v}(x,v)\) for a given state. More...

virtual void	computeK (const OdeState &state)=0
	Evaluation of \(K = -\frac{\partial f}{\partial x}(x,v)\) for a given state. More...

virtual void	computeFMDK (const OdeState &state)=0
	Evaluation of \(f(x,v)\), \(M(x,v)\), \(D = -\frac{\partial f}{\partial v}(x,v)\) and \(K = -\frac{\partial f}{\partial x}(x,v)\). More...

Protected Attributes
std::shared_ptr< OdeState >	m_initialState
	The initial state (which defines the ODE initial conditions \((x0, v0)\)) More...

unsigned int	m_initState

Vector	m_f
	The vector containing \(f(x, v)\).

SparseMatrix	m_M
	The matrix \(M(x,v)\).

SparseMatrix	m_D
	The The matrix \(D = -\frac{\partial f}{\partial v}(x,v)\).

SparseMatrix	m_K
	The The matrix \(K = -\frac{\partial f}{\partial x}(x,v)\).

Detailed Description

Ode equation of 2nd order of the form \(M(x,v).a = F(x, v)\) with \((x0, v0)\) for initial conditions and a set of boundary conditions.

The problem is called a Boundary Value Problem (BVP). This ode equation is solved as an ode of order 1 by defining the state vector \(y = \left(\begin{array}{c}x\\v\end{array}\right)\):

\[ y' = \left(\begin{array}{c} x' \\ v' \end{array}\right) = \left(\begin{array}{c} v \\ M(x, v)^{-1}.f(t, x, v) \end{array}\right) \]

Note: To allow the use of explicit and implicit solver, we need to be able to evaluate; \(M(x, v)\), \(f(t, x, v)\) but also \(K = -dF/dx(x, v)\) and \(D = -dF/dv(x, v)\); Models wanting the use of implicit solvers will need to compute these Jacobian matrices.

Member Function Documentation

§ applyCompliance()

virtual Matrix SurgSim::Math::OdeEquation::applyCompliance	(	const OdeState &	state,
		const Matrix &	b
	)

pure virtual

Calculate the product \(C.b\) where \(C\) is the compliance matrix with boundary conditions applied.

Note that this can be rewritten as \((B^T)(M^{-1})(B.b) = (B^T)((M^{-1})(B.b)) = x\), where \((M^{-1})(B.b) = y\) is simply the solution to \(M.y = B.b\) and \(B^T.y = x\).

Parameters

state	\((x, v)\) the current position and velocity to evaluate the various terms with
b	The input matrix

Returns: The matrix \(C.b\)

Implemented in SurgSim::Math::OdeComplexNonLinear, SurgSim::Math::MassPointsForStatic, SurgSim::Physics::FemRepresentation, SurgSim::Physics::DeformableRepresentation, and SurgSim::Math::MassPoint.

§ computeD()

virtual void SurgSim::Math::OdeEquation::computeD ( const OdeState & state )

protectedpure virtual

Evaluation of \(D = -\frac{\partial f}{\partial v}(x,v)\) for a given state.

Parameters

state \((x, v)\) the current position and velocity to evaluate the Jacobian matrix with

Implemented in SurgSim::Math::OdeComplexNonLinear, SurgSim::Physics::MockDeformableRepresentation, SurgSim::Physics::FemRepresentation, SurgSim::Math::MassPointsForStatic, SurgSim::Physics::MassSpringRepresentation, and SurgSim::Math::MassPoint.

§ computeF()

virtual void SurgSim::Math::OdeEquation::computeF ( const OdeState & state )

protectedpure virtual

Evaluation of the RHS function \(f(x, v)\) for a given state.

Parameters

state \((x, v)\) the current position and velocity to evaluate the function \(f(x,v)\) with

Implemented in SurgSim::Math::OdeComplexNonLinear, SurgSim::Physics::MockDeformableRepresentation, SurgSim::Physics::FemRepresentation, SurgSim::Physics::MassSpringRepresentation, SurgSim::Math::MassPointsForStatic, and SurgSim::Math::MassPoint.

§ computeFMDK()

virtual void SurgSim::Math::OdeEquation::computeFMDK ( const OdeState & state )

protectedpure virtual

Evaluation of \(f(x,v)\), \(M(x,v)\), \(D = -\frac{\partial f}{\partial v}(x,v)\) and \(K = -\frac{\partial f}{\partial x}(x,v)\).

When all the terms are needed, this method can perform optimization in evaluating everything together

Parameters

state \((x, v)\) the current position and velocity to evaluate the various terms with

Note: computeF(), computeM(), computeD(), computeK()

Implemented in SurgSim::Math::OdeComplexNonLinear, SurgSim::Math::MassPointsForStatic, SurgSim::Physics::FemRepresentation, SurgSim::Physics::MockDeformableRepresentation, SurgSim::Physics::MassSpringRepresentation, and SurgSim::Math::MassPoint.

§ computeK()

virtual void SurgSim::Math::OdeEquation::computeK ( const OdeState & state )

protectedpure virtual

Evaluation of \(K = -\frac{\partial f}{\partial x}(x,v)\) for a given state.

Parameters

state \((x, v)\) the current position and velocity to evaluate the Jacobian matrix with

Implemented in SurgSim::Math::OdeComplexNonLinear, SurgSim::Physics::FemRepresentation, SurgSim::Physics::MockDeformableRepresentation, SurgSim::Math::MassPointsForStatic, SurgSim::Physics::MassSpringRepresentation, and SurgSim::Math::MassPoint.

§ computeM()

virtual void SurgSim::Math::OdeEquation::computeM ( const OdeState & state )

protectedpure virtual

Evaluation of the LHS matrix \(M(x,v)\) for a given state.

Parameters

state \((x, v)\) the current position and velocity to evaluate the matrix \(M(x,v)\) with

Implemented in SurgSim::Math::OdeComplexNonLinear, SurgSim::Physics::MockDeformableRepresentation, SurgSim::Physics::FemRepresentation, SurgSim::Physics::MassSpringRepresentation, SurgSim::Math::MassPointsForStatic, and SurgSim::Math::MassPoint.

§ getD()

const SparseMatrix & SurgSim::Math::OdeEquation::getD ( ) const

Returns: The matrix \(D = -\frac{\partial f}{\partial v}(x,v)\)

§ getF()

const Vector & SurgSim::Math::OdeEquation::getF ( ) const

Returns: The vector containing \(f(x, v)\)

§ getInitialState()

const std::shared_ptr< OdeState > SurgSim::Math::OdeEquation::getInitialState ( ) const

Retrieves the ode initial conditions \((x0, v0)\) (i.e the initial state)

Returns: The initial state

§ getK()

const SparseMatrix & SurgSim::Math::OdeEquation::getK ( ) const

Returns: The matrix \(K = -\frac{\partial f}{\partial x}(x,v)\)

§ getM()

const SparseMatrix & SurgSim::Math::OdeEquation::getM ( ) const

Returns: The matrix \(M(x,v)\)

§ updateFMDK()

void SurgSim::Math::OdeEquation::updateFMDK	(	const OdeState &	state,
		int	options
	)

virtual

Update the OdeEquation (and support data) based on the given state.

Parameters

state	\((x, v)\) the current position and velocity to evaluate the various terms with
options	Flag to specify which of F, M, D, K needs to be updated.

Reimplemented in SurgSim::Physics::FemRepresentation.

Member Data Documentation

§ m_initialState

std::shared_ptr<OdeState> SurgSim::Math::OdeEquation::m_initialState

protected

The initial state (which defines the ODE initial conditions \((x0, v0)\))

Note: MUST be set by the derived classes

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

SurgSim/Math/OdeEquation.h
SurgSim/Math/OdeEquation.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Function Documentation

§ applyCompliance()

§ computeD()

§ computeF()

§ computeFMDK()

§ computeK()

§ computeM()

§ getD()

§ getF()

§ getInitialState()

§ getK()

§ getM()

§ updateFMDK()

Member Data Documentation

§ m_initialState