Alan, I've browsed this text a little, but to be honest, I was unable to see the direct advantage of such an approach, at least for the type of work I'm involved with. I'm willing to trust that the mathematics are cleaner and more complete, but I'm curious what the advantage is in the end. Do you know specific types of systems that really benefit from this approach? I am currently studying the rolling torus and the Whipple bicycle model, and I would be curious to see how the GA approach would compare to a more classical approach. Have you seen the GA approach applied to classical examples like the rolling disc or torus, or any other nonholonomic systetms?
Also, I have another text in electronic format called Geometric Algebra with Applications in Engineering, by Christian Perwass. Are you familiar with it? If so, do you recommend it as an alternative to the book by Doran and Lasenby? Or is Doran and Lasenby available electronically? Thanks, ~Luke On Jun 1, 2:25 pm, Alan Bromborsky <abro...@verizon.net> wrote: > Luke wrote: > > If you are familiar with Autolev, then you are probably familiar with > > some of the behavior that makes it very convenient and easy to derive > > equations of motion in. You might also be familiar with some of its > > limitations. One of the main goals of PyDy is to replicate (in a more > > Pythonic way) the features of Autolev, and improve upon its > > deficiencies. One of the main things I have implemented so far that > > is very useful is the 12 Euler and 12 Space fixed rotation > > conventions, into a convenient framework for working with vector > > expressions without having to deal with the rotation matrices / > > transformations explicitly. This makes many things much simpler when > > defining your problem. > > > I would love to hear your input on feature requests or overall design > > approaches for PyDy. Here is all the group information: > > *http://groups.google.com/group/pydy > > * p...@googlegroups.com > > *http://dlpeterson.com/blog > > > I have classes for ReferenceFrame and am working on the Point class, > > my idea is to implement methods for each of these classes that can > > assign inertia and/or torque (ReferenceFrame) and mass and/or force > > (Point), which, combined with the kinematics of the problem, will > > allow for Kane's method to be utilized and the equations of motion > > generated in a very algorithmic and systematic fashion. > > > There are already a few example problems up there, but if you think > > any others, I'd be happy to put them up -- the more the better. > > > ~Luke > > > On May 29, 9:56 pm, "2006.uchida" <2006.uch...@gmail.com> wrote: > > >> Thank you for your response. I first knew Autolev. > >> I took a look at one of the sample test codes of Pydy named > >> "simplependulum.py" and didn't look into the details but it appears > >> that it allows us to obtain motion equations and simulations by only > >> connecting the class instances that represent rigid bodies, sorry if I > >> misunderstand. > >> It is a cool idea! We no longer need to transform the coordinates nor > >> to calculate the absolute positions of the rigid objects one by one, > >> which is a hard part for me in using Kane's method. Moreover, it also > >> provides the dynamics simulations as well as the equations. We can do > >> a simulation without thinking about programming for the integration of > >> the simulation. > >> I think it would be good to design the interface using a class that > >> represent a kind of rigid bodies, links, forces, or any other > >> extentions with understandable, short names and to make the setup for > >> the usage easy like all that we have to do to use the feature is only > >> to make up the relations of the class instances. > >> Anyway, it would already make our life easier. > > >> On 5月24日, 午前6:06, Luke <hazelnu...@gmail.com> wrote: > > >>> This is cool, it is good to see other people who are familiar with > >>> Kane's method, there aren't many of us :) > > >>> Are you familiar with Autolev? With PyDy, I am working to achieve > >>> some of the same behavior as Autolev, but make it even better, and > >>> have a lot more features. I'd love to hear your input on design > >>> choices for PyDy if you have the time. Right now I'm working on > >>> extending it to allow for the 12 different Euler angles, and the 12 > >>> different space fixed angles, Euler parameters, Rodrigues parameters, > >>> and axis/angle rotations. The major work to take care of kinematics > >>> automatically is in place, but there is definitely more to do in > >>> regards to how to deal with constraints, definitions of generalized > >>> speeds, etc... > > >>> What sort of systems do you use Kane's method to study? My own area > >>> of research is two wheeled vehicle (bicycle/motorcycle) dynamics and > >>> control. > > >>> ~Luke > > >>> On May 23, 6:06 am, "2006.uchida" <2006.uch...@gmail.com> wrote: > > >>>> I made a small script in MuPAD few years ago but I had to say goodbye > >>>> to MuPAD last November, so I found Sympy and have translated it into > >>>> Sympy now. I want to share it and I'm happy if I get some comments. > > >>>> What I made is the small script that generates motion equations for > >>>> multibody dynamics by using Kane's method. It handles multibody > >>>> dynamics, the dynamic behavior created with several rigid bodies that > >>>> are interconnected, for instance, double pendulum, robot arms, crank > >>>> mechanism, etc. The script allows you to get the equation easily by > >>>> setting some information of masses, positions, forces, etc. > > >>>> available for download from > >>>> here:http://www.esnips.com/doc/0960cb0a-8820-4169-b582-d58a2d6c5f28/MoEqGe... > > >>>> Here is a sample code and results. More details, please see the file > >>>> "smple.py" which you can download above. > > >>>> [Code] > >>>> import sympy > >>>> import motionequation > > >>>> def main(): > > >>>> # Sample for Newton's second law > > >>>> mat = sympy.Matrix > >>>> t, x, m, f = sympy.symbols( > >>>> "t, x, m, f") > > >>>> pos_vec = mat([x(t),0,0]) > >>>> force_vec = mat([f(t),0,0]) > >>>> I_mat = sympy.zeros(3) > >>>> ome_vec = sympy.zeros([3,1]) > >>>> torque_vec = sympy.zeros([3,1]) > > >>>> result = motionequation.get_withKane( > >>>> t, [x(t).diff(t)], [m], > >>>> [pos_vec], > >>>> [I_mat], > >>>> [ome_vec], > >>>> [pos_vec], [force_vec], > >>>> [ome_vec], [torque_vec]) > > >>>> print "Newton's second law: " > >>>> sympy.pprint(result) > > >>>> main() > >>>> [/Code] > > >>>> [Console] > >>>> Newton's second law: > >>>> 2 > >>>> d > >>>> [m*-----(x(t)) = f(t)] > >>>> dt dt > >>>> [/Console] > > >>>> You can use the feature by calling the function get_withKane in the > >>>> module motionequation. I tried and confirmed that it will return > >>>> several kinds of the motion equations, for example, Newton's second > >>>> law, Euler's equations of rigid body, etc. > > >>>> ondrej.certik provided me with useful information on the project for > >>>> such a feature which is found at:http://code.google.com/p/pydy/ > > >>>> I'm going to write more about how to specify the arguments of the > >>>> function to use for your own project. > > You might want to look in "Geometric Algebra for Physicists" by Doran > and Lasenby, Chapter 3 - Classical Mechanics. Especially look at the way > rotations can be handled. For example the spinor equations for planetary > motion are harmonic oscillators. Geometric algebra is being used in > robotics to simplify the modeling of robotic arms, etc. Another thing to > look at is conformal geometry (Chapter 10) where 3-dimensions are mapped > to 5-dimensions, but translations, scaling, and rotations in > 3-dimensions become rotations of null vectors in 5-dimensions. --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sympy?hl=en -~----------~----~----~----~------~----~------~--~---
