Peter, Yes, the velocity constraints work the same way. There are reaction forces that constrain the velocities.
Jason moorepants.info +01 530-601-9791 On Thu, Feb 3, 2022 at 10:37 AM Peter Stahlecker <peter.stahlec...@gmail.com> wrote: > Dear Jason, > > Thanks! > If I understood correctly, if I use velocity constraints, I do not use the > minimal number of generalized coordinates, hence these reaction forces and > 'virtual' speeds appear in my force term of the equations of motion. As > they are normal to the motion of the particle(s), I simply set them to zero > in the force term. > > Peter > > moore...@gmail.com schrieb am Donnerstag, 3. Februar 2022 um 10:20:46 > UTC+1: > >> Peter, >> >> If you have a particle that is forced to move along a path (typically be >> a configuration constraint), then there exists reaction forces normal to >> the path that keep it on the path. These forces are not present in the >> equations of motion when they are formed with minimal coordinates. But you >> can expose the forces by introducing fictitious (auxiliary) generalized >> speeds normal to the path and a variable for the forces. This will result >> in the minimal equations of motion and some algebraic equations for the >> forces. All of these equations will have the aux speeds, which then must be >> set to zero because they are fictitious. This should then leave you with >> the equations of motion plus some equations that can be solved for the >> forces. >> >> Jason >> moorepants.info >> +01 530-601-9791 <(530)%20601-9791> >> >> >> On Thu, Feb 3, 2022 at 10:03 AM Peter Stahlecker <peter.st...@gmail.com> >> wrote: >> >>> Thanks! Would I also set the 'reaction forces' appearing in the force >>> term equal to zero? >>> As per my understanding of mechanics, they also should have no influence >>> on the equations of motion (?) >>> >>> moore...@gmail.com schrieb am Donnerstag, 3. Februar 2022 um 09:59:53 >>> UTC+1: >>> >>>> The virtual speeds will appear in the force equations, but you then >>>> just set them to zero because they are fictitious. You force equation >>>> should then be correct. >>>> >>>> Jason >>>> moorepants.info >>>> +01 530-601-9791 <(530)%20601-9791> >>>> >>>> >>>> On Thu, Feb 3, 2022 at 9:58 AM Peter Stahlecker <peter.st...@gmail.com> >>>> wrote: >>>> >>>>> When I use a velocity constraint to force a particle not to move in a >>>>> certain direction, there must be a 'reaction force' on the particle. >>>>> I use KM.auxiliary_eqs to find reaction forces, which works very well >>>>> in general! >>>>> >>>>> However, if I try to find the reaction force due to a velocity >>>>> constraint, it does no seem to work: >>>>> The force term of the equations of motion contains the 'virtual >>>>> speed', its time derivative and the reaction force. >>>>> >>>>> Am I doing something wrong, or do velocity_constraints and >>>>> KM.auxiliary_eqs just not work together? >>>>> I attach some code, showing my problem. >>>>> >>>>> *Any help is greatly appreciated!* >>>>> >>>>> -- >>>>> 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+un...@googlegroups.com. >>>>> To view this discussion on the web visit >>>>> https://groups.google.com/d/msgid/sympy/e8091bb4-9730-4dc2-8e31-59662ef09e56n%40googlegroups.com >>>>> <https://groups.google.com/d/msgid/sympy/e8091bb4-9730-4dc2-8e31-59662ef09e56n%40googlegroups.com?utm_medium=email&utm_source=footer> >>>>> . >>>>> >>>> -- >>> 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+un...@googlegroups.com. >>> >> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/sympy/5b2301f3-8dc7-4e69-9a52-31f5d235daban%40googlegroups.com >>> <https://groups.google.com/d/msgid/sympy/5b2301f3-8dc7-4e69-9a52-31f5d235daban%40googlegroups.com?utm_medium=email&utm_source=footer> >>> . >>> >> -- > 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/aa252785-8644-40a6-afe9-c7a817388500n%40googlegroups.com > <https://groups.google.com/d/msgid/sympy/aa252785-8644-40a6-afe9-c7a817388500n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- 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/CAP7f1AiNUGcpQx-8X4xoZp0ezT7%2Bgm_q8ZZpKmTwTGYix9qiGA%40mail.gmail.com.
