Oscar, There are essentially two approaches in computational multibody dynamics to arrive at the equations of motion: symbolic first (what SymPy does) or fully numeric (tools like Simbody, Bullet, etc.). You have to calculate derivatives with respect to the coordinates of the system to get Newton and Euler's dynamical equations, thus having the symbolic expressions is one way to calculate those derivatives. The rotations have to be parameterized symbolically for this approach. This is how sympy.physics.mechanics works. The rotations can be designed as quaternions, Euler angles, Rodriguez parameters, Euler parameters, or many other ways, but you still have to compute the derivatives of these symbolically parameterized rotations.
Peter's number of operations is very small compared to many other more complicated multibody problems. Jason moorepants.info +01 530-601-9791 On Tue, Jun 29, 2021 at 1:09 PM Oscar Benjamin <oscar.j.benja...@gmail.com> wrote: > How do the op counts get into the tens or hundreds of thousands? > > When the expressions are that complicated I would have thought that it > was faster and more numerically accurate to perform whatever symbolic > operations are used to obtain those expressions using numerical > routines. For example if a matrix is inverted symbolically it would be > better to substitute your values and invert the matrix numerically > etc. A 3D rotation can be computed very cheaply in floating point with > quaternions. > > -- > Oscar > > On Tue, 29 Jun 2021 at 12:00, Peter Stahlecker > <peter.stahlec...@gmail.com> wrote: > > > > Dear Jason, > > > > Thanks! > > I tested it right away, and I counted the operations of an entry of rhs > = KM.rhs() > > > > For ‚Body‘ I got the count 245,633 > > With the auxiliary frames the count was 13,235 > > > > Thanks again and stay healthy! > > > > I will keep on testing this. > > > > Peter > > > > > > > > > > On Tue 29. Jun 2021 at 12:32 Jason Moore <moorepa...@gmail.com> wrote: > >> > >> Peter, > >> > >> THey are equivalent other than one may provide a simpler set of > direction cosine matrices and angular velocity definitions. The "Body" > method should give simpler equations of motion in the end because we try to > use pre-simplified forms of the equations. I don't know why you'd see > faster with the intermediate frame method. > >> > >> You can use sympy's count_ops() function to see how many operations > each symbolic form gives. The one with more operations should ultimately be > slower when lambdified(). > >> > >> Jason > >> moorepants.info > >> +01 530-601-9791 > >> > >> > >> On Tue, Jun 29, 2021 at 5:09 AM Peter Stahlecker < > peter.stahlec...@gmail.com> wrote: > >>> > >>> When I want to do this, it seems to me there are these possibilities: > >>> > >>> 1. > >>> A = N.orientnew(‚A‘, ‚Body‘, [q1, q2, q3], ‚123‘) > >>> This does it in one step > >>> > >>> 2. > >>> I use two intermediate frames and use the word ‚Axis‘ instead of ‚Body‘ > >>> > >>> Geometrically, this should be the same, but it seems to me, that with > the intermediate frames establishing Kane‘s equations, lambdifying them and > doing the numerical integration is MUCH faster. > >>> > >>> Are methods 1 and 2 not equivalent, as I assumed, or am I doing > something wrong? > >>> > >>> Thanks for any explanation! > >>> > >>> -- > >>> You received this message because you are subscribed to the Google > Groups "sympy" group. > >>> To unsubscribe from this group and stop receiving emails from it, send > an email to sympy+unsubscr...@googlegroups.com. > >>> To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/d1597154-f8a8-42fa-b29b-6e8f57062441n%40googlegroups.com > . > >> > >> -- > >> You received this message because you are subscribed to the Google > Groups "sympy" group. > >> To unsubscribe from this group and stop receiving emails from it, send > an email to sympy+unsubscr...@googlegroups.com. > >> To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAP7f1AhvTHkfn8_Wc7L9i7em3QvDHn6MPBHoWwqvK9qOUw3QfA%40mail.gmail.com > . > > > > -- > > Best regards, > > > > Peter Stahlecker > > > > -- > > You received this message because you are subscribed to the Google > Groups "sympy" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to sympy+unsubscr...@googlegroups.com. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CABKqA0bdrLLiCY7w3yG_3sPTmx7O4Z00tn-mLSssj0rvT4m9QA%40mail.gmail.com > . > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAHVvXxSchAaF6rRig0zL9VF4w3MLyiVra2dZ4vp9vuYDdKyY0w%40mail.gmail.com > . > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAP7f1AiQAxfON4_KJPhP%2BwuftBAzop2nKVMppwU1keAf08xPPQ%40mail.gmail.com.
