Re: Rigid Body dynamics and solution methods

Preben wrote:
Just to sum up what I really have done... It seems like this could be an
advantage for me and you.

Now I solve the systems of equations:

M * mu = - F - T

to find the constraint force multipliers and next calculate the
accelerations :

ublas::vector<double> accel = -dV + prod(trans(dG), mu);
for (unsigned int i = 0; i < m.size(); ++i) {
accel(i) = accel(i)/m(i);
}

now it should be possible to use a method for solving the equations of
motion!


Is this a bad method?

It is not completely wrong, but it has enabled you to ignore a very pertinent
fact, namely that the accelerations depend on the velocities. In a pure
rigid-body case these terms give rise to centripetal and Coriolis-like
forces.

If you attempt to integrate such a Hamiltonian in generalised
co-ordinates using standard velocity-Verlet or any other straightforward
integration algorithm you will find that energy is not conserved. This
is because you are implicitly using the velocities from step n but
co-ordinates from n+1 to evaluate the accelerations. Please re-read
my earlier posting where you will find a better discussion of this issue.

Keith Refson

--
Dr Keith Refson,
Building R3
Rutherford Appleton Laboratory
Chilton
Didcot kr AT
Oxfordshire OX11 0QX isise D@T rl D.T ac D?T uk
.

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