Equations of Motion for a Torsional 2DOF System Using Newton's 2nd Law and Lagrange's Equations
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- Опубликовано: 22 мар 2018
- Deriving the equations of motion for a two degree-of-freedom torsional system two ways - using first Newton's 2nd Law and then the Method of Lagrange's Equations.
This channel is such a boon! Please continue the good work.. Thank you.
Excellent explanation of similarity between two methods.
Thank you! :)
Thank You sir, it is way better than going to class. I mean I can learn it by watching this, and it really helps me ;)
Thank you so much for this video lecture.
Thank you!
thank you very much that was helpful
Your videos are great. Please keep doing these kind of clips.
May I suggest you attack some aeroelasticity problems? They are very similar, and I know you have an aerospace background.
Yes. That was my eventual plan...to get to the computer simulation of some aeroelasticity problems (which is my field). Wanted to get there from a computational point-of-view rather rather than just analytically. First I think I need to make a short series on aero - perhaps panel methods and perhaps CFD eventually. Then I can couple the aero and structural models. Along the way I will definitely make a video of a simple aeroelastic analysis using a 2 d.o.f. model and basic aero.
Using the standard way of deriving the ODE for the system (i.e not using the Lagrangian method), why is it that the (theta_1 - theta_2) terms flipped for the both of the FBD of the two discs? In other words, why is it that the contribution of the second spring constant for the first FBD is Kt_2(theta_1 - theta_2) while the second spring constant for the second FBD is Kt_2(theta_2 - theta_1)? Is it assumed that one disc is twisted more than the other?
The is no assumption to the relative twist of each disk. The reason for the difference in signs in the moment comes from Newton's 3rd Law. The force (or moment) experienced by one mass is equal and opposite to the force/moment on the other mass.
when differentiating L equation wrt theta_1, why are the signs in front of kt1 and kt2 flipped?
The 2nd term in Lagrange's Equation (eqn 3) shows that we need to subtract this part. This is what flips the signs.