All Questions
6 questions
1
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Relation between fixed constraints and time derivative of the Lagrangian
I have had some trouble interpreting and proving the following statement from Fasano, Marmi's "Analytical Mechanics" (page 139):
"... ${\partial L}/{\partial t} \neq 0$ (1) only if the ...
- 402
1
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0
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29
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Explicit Example of Computing the Action [closed]
I have been dealing with this problem for awhile and I have almost given up. I am asked to compute the action for a free particle going from $x = x_0 = 0$ at time $t = t_0=0$ to its end point $x = x_1 ...
- 923
1
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2
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461
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Lagrangian Dynamics of an inverted Spherical Cart Pendulum
Introduction
I have to come up with a PD-controller for an inverted Spherical Cart Pendulum, therefore I tried to compute the Dynamics of such a Pendulum.
The Spherical Cart Pendulum is a hybrid ...
1
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0
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136
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Difference between eigenvalues of the potential energy Hessian vs. "generalized" eigenvalues with respect to a kinetic energy "metric"
Simple version
Consider if we have a Lagrangian defined by
$$L(q,\dot{q}) = \frac{1}{2} g_{ij}(q) \dot{q}^i \dot{q}^j - U(q) \tag{1a}$$
where the potential energy $U(q)$ has a single minimum at $q=0$ (...
- 3,780
0
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1
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148
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Rigid bodies: angular velocities, momentum, Inertia Tensor, rotational kinetic energy. Books suggestions? [duplicate]
I'm having a hard time with understanding how to model the rotational kinetic energy of rigid bodies. I will appreciate any good suggestion about resources such as books or videos regarding topics ...
2
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1
answer
582
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Motion equations for Woodpecker toy (multibody system)
I am trying to understand a rigid multibody model of a Woodpecker toy (see figure below). Now I am not going to go into details about the model or justify this approach, I am just trying to understand ...
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