Dear Oskar, It is just one 3D pendulum, one body only. I have no idea, how big these terms should be.
I am doing this for no other purpose than to spend some time in my semi retirement stage. (I studied mechanical engineering 45 years ago). If find this sumpy Kane's method fascinating! I never looked at these quaternions, because we did not use them when I studied. Maybe I should do it. Take care, Peter On Tue 29. Jun 2021 at 14:09, 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 > . > -- 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/CABKqA0YU9scxVPj4E-SNx3Ka4-yATQd8WS1u5BPZskN-pkqpSg%40mail.gmail.com.
