Simbody
3.7

This is a strippeddown numerical integrator for small ODE or DAE problems whose size is known at compile time, with no provision for discrete variables, event detection, or interpolation. More...
Public Types  
enum  { NQ = Eqn::NQ, NC = Eqn::NC, N = 2*NQ } 
Public Member Functions  
GeodesicIntegrator (const Eqn &eqn, Real accuracy, Real constraintTol)  
Construct an integrator for the given set of equations eqn, which are to be solved to the given accuracy, with constraints maintained to within the given constraintTol. More...  
void  initialize (Real t, const Vec< N > &y) 
Call this once before taking a series of steps. More...  
void  setTimeAndState (Real t, const Vec< N > &y) 
Set initial time and state prior to integrating. More...  
void  setNextStepSizeToTry (Real h) 
Use this if you think you know a better initial step size to try than the default. More...  
Real  getNextStepSizeToTry () const 
Return the size of the next time step the integrator will attempt on the next call to takeOneStep(). More...  
Real  getRequiredAccuracy () const 
Return the accuracy requirement as set in the constructor. More...  
Real  getConstraintTolerance () const 
Return the constraint tolerance as set in the constructor. More...  
Real  getActualInitialStepSizeTaken () const 
Return the size of the first accepted step to be taken after the most recent initialize() call. More...  
int  getNumStepsTaken () const 
Return the number of successful time steps taken since the most recent initialize() call. More...  
int  getNumStepsAttempted () const 
Return the total number of steps that were attempted since the most recent initialize() call. More...  
int  getNumErrorTestFailures () const 
How many steps were rejected because they did not satisfy the accuracy requirement, since the most recent initialize() call. More...  
int  getNumProjectionFailures () const 
How many steps were rejected because the projectIfNeeded() method was unable to satisfy the constraint tolerance (since the most recent initialize() call). More...  
int  getNumInitializations () const 
Return the number of calls to initialize() since construction of this integrator object. More...  
void  takeOneStep (Real tStop) 
Advance time and state by one errorcontrolled step and return, but in no case advance past t=tStop. More...  
const Real &  getTime () const 
Return the current time. More...  
const Vec< N > &  getY () const 
Return the complete current state as a Vec<N>. More...  
const Vec< NQ > &  getQ () const 
Return just the "position" variables q from the current state. More...  
const Vec< NQ > &  getU () const 
Return just the "velocity" variables u from the current state. More...  
const Vec< N > &  getYDot () const 
Return the complete set of time derivatives of the current state. More...  
const Vec< NQ > &  getQDot () const 
Return just the derivatives qdot of the "position" variables q. More...  
const Vec< NQ > &  getUDot () const 
Return just the derivatives udot of the "velocity" variables u. More...  
Static Public Member Functions  
template<int Z>  
static Real  calcNormInf (const Vec< Z > &v) 
This is a utility routine that returns the infinity norm (maximum absolute value) contained in a fixedsize, scalar Vec. More...  
template<int Z>  
static Real  calcNormRMS (const Vec< Z > &v) 
This is a utility routine that returns the RMS norm of a fixedsize, scalar Vec. More...  
This is a strippeddown numerical integrator for small ODE or DAE problems whose size is known at compile time, with no provision for discrete variables, event detection, or interpolation.
You cannot use this integrator to advance a Simbody System; see Integrator instead. Everything is defined in this header file so that the integration can proceed with virtually no overhead. Templates are used rather than runtime polymorphism, so there are no virtual function calls. The system of equations is given as a template object that must implement particular methods which the compiler may inline if they are simple enough.
This integrator is instantiated with a class that encapsulates the system of equations to be solved, and must provide compile time constants and methods with the following signatures:
This is an explicit, variablestep integrator solving a 2ndorder DAE structured as an ODEonamanifold system[1] like this:
(1) udot = f(t,q,u) NQ dynamic differential equations (2) qdot = u NQ kinematic differential equations (3) 0 = c(t,q,u) NC constraints
Here the "dot" suffix indicates differentiation with respect to the independent variable t which we'll refer to as time here although it can be anything (for geodesic calculations it is arc length). We'll
call the second order variables q the "position variables", and their time derivatives u the "velocity variables". Collected together we call the state y={q,u}. At the beginning of a step, we expect to have been given initial conditions t0,q0,u0 such that c(t0,q0,u0)<=tol. The user provides the accuracy requirement and constraint tolerance. We solve the system to that accuracy while keeping the constraints within tolerance. The integrator returns after taking a successful step which may involve trial evaluations that are retracted.
By "ODE on a manifold" we mean that the ODE (1,2) automatically satisfies the condition that IF c==0, THEN cdot=0, where
cdot=Dc/Dt + Dc/Dq*qdot + Dc/Du*udot
This means that satisfaction of the accelerationlevel constraints is built into the dynamic differential equations (1) so that we need only deal with relatively slow drift of the solution away from the position and velocity constraint manifolds.
To handle the constraint drift we use the method of coordinate projection and expect the supplied Equations object to be able to perform a leastsquares projection of a state (q,u) to move it onto the constraint manifolds.
[1] Hairer, Lubich, Wanner, "Geometric Numerical Integration: StructurePreserving Algorithms for Ordinary Differential Equations", 2nd ed., section IV.4, pg 109ff, Springer, 2006.

inline 
Construct an integrator for the given set of equations eqn, which are to be solved to the given accuracy, with constraints maintained to within the given constraintTol.

inline 
Call this once before taking a series of steps.
This sets the initial conditions, and calculates the starting derivatives and constraint errors. The constraints must be satisfied already by the given state; an error is thrown if not.

inline 
Set initial time and state prior to integrating.
State derivatives and constraint errors are calculated and an error is thrown if the constraints are not already satisifed to the required tolerance.

inline 
Use this if you think you know a better initial step size to try than the default.

inline 
Return the size of the next time step the integrator will attempt on the next call to takeOneStep().

inline 
Return the accuracy requirement as set in the constructor.

inline 
Return the constraint tolerance as set in the constructor.

inline 
Return the size of the first accepted step to be taken after the most recent initialize() call.

inline 
Return the number of successful time steps taken since the most recent initialize() call.

inline 
Return the total number of steps that were attempted since the most recent initialize() call.
In general this will be more than the number of steps taken since some will be rejected.

inline 
How many steps were rejected because they did not satisfy the accuracy requirement, since the most recent initialize() call.
This is common but for nonstiff systems should be only a modest fraction of the number of steps taken.

inline 
How many steps were rejected because the projectIfNeeded() method was unable to satisfy the constraint tolerance (since the most recent initialize() call).
This should be very rare.

inline 
Return the number of calls to initialize() since construction of this integrator object.
void SimTK::GeodesicIntegrator< Eqn >::takeOneStep  (  Real  tStop  ) 
Advance time and state by one errorcontrolled step and return, but in no case advance past t=tStop.
The integrator's internal time, state, and state derivatives are advanced to the end of the step. If this step reaches tStop, the returned time will be exactly tStop.

inline 
Return the current time.

inline 
Return the complete current state as a Vec<N>.

inline 
Return just the "position" variables q from the current state.

inline 
Return just the "velocity" variables u from the current state.

inline 
Return the complete set of time derivatives of the current state.

inline 
Return just the derivatives qdot of the "position" variables q.

inline 
Return just the derivatives udot of the "velocity" variables u.

inlinestatic 
This is a utility routine that returns the infinity norm (maximum absolute value) contained in a fixedsize, scalar Vec.

inlinestatic 
This is a utility routine that returns the RMS norm of a fixedsize, scalar Vec.