Mechanics Rolling disc with Kanes method

[aliko]

Hi! 

I'm trying to get into mechanics module of sympy.

Can someone point me on a better way to add uneven terrain to example of rolling disc with Kanes method (http://docs.sympy.org/latest/modules/physics/mechanics/examples/rollingdisc_example_kane.html)? 

For example I could have an inclination of terrain 'alpha' as a smooth function of q3 (disc angle of rotation). Should I introduce new variable to equations? Or account for alpha somewhere else?

Great thanks in advance!

[Jason Moore]

The rolling disc examples in the docs make the assumption that the contact point is always located in a plane normal to gravity. If you want to generalize that then you need to remove that assumption. I don't think it is a good idea to have the surface be a function of the rotation angle. It could certainly make for some crazy dynamics, but it doesn't sound realistic. In general, you need the definition of a surface, either a function z=f(x, y) or a look-up table that provides z as a function of x and y. This surface needs to have some orientation relative to gravity defined. Then you must constrain the disc to not penetrate the surface. These kinds of constraints are probably easier by doing "soft" dynamics and are much hairier when you have to work out the non-deformable contact, especially when the disc touches the surface at more than one point. The general problem you describe is not at all trivial. What are you trying to accomplish? If I knew the scope of what you want to know maybe there is an easier path I can suggest.

Jason
moorepants.info
+01 530-601-9791

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[aliko]

Hi Jason! Thank you for quick response!

I'm trying to describe a motion of some sort of one wheeled vehicle. It doesn't matter what is the surface of all the terraing but it does matter what are the unevenness on the way of the wheel. So trying to keep things as simple as possible I think about including one more parameter - the inclination of road on the path of the wheel no matter how it turns. The goal is to understand how such unevenness influences dynamics. Of course the inclination on the path should change slowly to guarantee only one point of contact. Is such approach feasible?

Also I would like to know how to apply the torque if  I have a motor on axis. There is a gravity force applied to center of mass in the example but no examples on how to apply torque.

By the way, your page is great, you making cool things!) I've learned about pydy from it will look at it closer)

вторник, 9 декабря 2014 г., 23:14:11 UTC+3 пользователь Jason Moore написал:

[aliko]

As for second question about including external torques I've found all I need in your tutorials on github. Thanks for that alot!

As for first question looking forward to hear from you your oppinion!

Thanks in advance!

среда, 10 декабря 2014 г., 0:34:04 UTC+3 пользователь aliko написал: