All Questions
8
questions with no upvoted or accepted answers
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Meaning of 2 kinetic energy terms in the equations
I have this problem (The two rods will be called links. Link 1 has length $a_1$ while link 2 has length $a_2$. The distance of the center of mass of each link to their respective joint is $l_i$):
And ...
1
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1
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88
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Energy of a system executing forced oscillations
In L&L's textbook of Mechanics (Vol. 1 of the Course in Theoretical Physics) $\S 22$ Forced oscillations, one finds the following statement:
\begin{equation}
\xi = \dot{x} + i \omega x, \tag{22.9}...
- 39
1
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1
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103
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Why Lagrangian is $L=\frac{1}{2}mv^2$ and not $mv^2$ for a free particle in an intertial frame? Both are proportional to the square of velocity
Landau writes the Lagrangian of a free particle in a second inertial frame as $$L(v'^{2})=L(v^2)+\frac{\partial L}{\partial v^2}2\textbf{v}\cdot{\epsilon},$$ and then it's written that the Lagrangian ...
- 41
1
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How is kinetic energy $T$ given by $T=\dfrac{1}{2}\sum_{i}p_{i}\dot{q_{i}}$ in Hamiltonian and Lagrangian mechanics?
Im going through a website teaching Hamiltonian mechanics and I know the below
$$-\dot{p}_{i}=\dfrac{\partial H}{\partial q_{i}} \tag{14.3.12}$$
$$\dot{q}_{i}=\dfrac{\partial H}{\partial p_{i}} \tag{...
- 1,270
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Difference between eigenvalues of the potential energy Hessian vs. "generalized" eigenvalues with respect to a kinetic energy "metric"
Simple version
Consider if we have a Lagrangian defined by
$$L(q,\dot{q}) = \frac{1}{2} g_{ij}(q) \dot{q}^i \dot{q}^j - U(q) \tag{1a}$$
where the potential energy $U(q)$ has a single minimum at $q=0$ (...
- 3,710
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Lagrangian of 2 masses connected by a spring
Given: 2 masses are connected by a spring and are sliding down a frictionless inclined plane. They also have a nonzero angular momentum about their COM.
My attempt:
$$L_{com}=T_{com}-U_{com}$$
$$=\...
- 1,183
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Question about Problem $12$ in Chapter $11$ from Kibble & Berkshire's book
I write again the problem for convinience:
A rigid rod of length $2a$ is suspended by two light, inextensible strings of length $l$ joining its ends to supports also a distance $2a$ apart and level ...
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Derivative of Action
How to show that partial derivative of action is Energy.
action of system $S[q_1,q_2, t_1, t_2]$ is integral by time of system Lagrangian. I need to show that partial derivatives by $t_1$ and $t_2$ is ...
