Timeline for Transformation of the dynamics of mechanical system under coordinate change
Current License: CC BY-SA 3.0
7 events
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| Jan 3, 2012 at 23:55 | history | edited | Jorge | CC BY-SA 3.0 |
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| Jan 3, 2012 at 22:57 | history | edited | Jorge | CC BY-SA 3.0 |
deleted 183 characters in body
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| Jan 3, 2012 at 22:53 | comment | added | user17945 | I agree with Ryan, though, this isn't really an appropriate question for this site. | |
| Jan 3, 2012 at 22:52 | comment | added | user17945 | There's quite a bit wrong here. My suggestion would be to write everything in coordinates: $q^i=h^i(y),\ \dot{q}^i = \frac{\partial h^i}{\partial y^m}\dot{y}^m,\ \ddot{q}^i=\frac{\partial h^i}{\partial y^m}\ddot{y}^m+\frac{\partial^2 h^i}{\partial y^n\partial y^n}\dot{y}^n\dot{y}^m$. Substitute this into $M(q)\ddot{q}+N(q,\dot{q})=u$, multiply everything by $J$, and massage what you get into the form $\hat{M}(y)\ddot{y}+\hat{N}(y,\dot{y}) = \hat{u}$. Your assumed transformation of $\hat{M}$ is correct, but $\hat{N}$ is way off (and $\hat{u}=J u$). | |
| Jan 3, 2012 at 22:51 | comment | added | Jorge | Ryan i'm not sure what you mean by motivation. From my end, my motivation is very clear: i'm doing research in nonlinear control & robotics and i'm investigating a very specific thing (the application of a specific map $q=h(y)$). However, tensorial analysis is not strong point and i'm not really sure about the last three equations. I could rephrase the question with a very specific argument: does the inertia tensor and the Coriolis vector transform this way? However in order to provide a background, i've elaborated on the whole thing! | |
| Jan 3, 2012 at 21:50 | comment | added | Ryan Budney | Do you have a motivation? From the way you've written your question, it appears you're meandering around in a textbook and manipulating expressions, looking for people to tell you whether or not you've made a mistake. MO is generally for more focused questions, rather than "please check my argument for errors" type requests. | |
| Jan 3, 2012 at 18:00 | history | asked | Jorge | CC BY-SA 3.0 |