All Questions
Tagged with classical-mechanics lagrangian-formalism
1,466
questions
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How do you know if a coordinate is cyclic if its generalized velocity is not present in the Lagrangian?
Goldstein's Classical Mechanics says that a cyclic coordinate is one that doesn't appear in the Lagrangian of the system, even though its generalized velocity may appear in it (emphasis mine). For ...
- 2,251
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Elementary derivation of the motion equations for an inverted pendulum on a cart
Consider a cart of mass $M$ constrained to move on the horizontal axis. A massless rod is attached to the midpoint of the cart, having a mass $m$ on its endpoint. See wikipedia for a picture and for a ...
- 173
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What is the significance of action?
What is the physical interpretation of
$$ \int_{t_1}^{t_2} (T -V) dt $$
where, $T$ is Kinetic Energy and $V$ is potential energy.
How does it give trajectory?
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Question about units in Lagrangian dynamics (inertia matrix)
I have a 3 degree of freedom system and my equation of motion is like this:
$$M(q)q_{dd} + C(q,q_d)q_d+G(q)~=~0$$
$M(q)$: inertia matrix
$C(q,q_d)$: Coriolis-centrifugal matrix
$G(q)$: potential ...
- 139
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Lagrangian of two particles connected with a spring, free to rotate
Two particles of different masses $m_1$ and $m_2$ are connected by a massless spring of spring constant $k$ and equilibrium length $d$. The system rests on a frictionless table and may both oscillate ...
- 2,212
16
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Hamilton-Jacobi Equation
In the Hamilton-Jacobi equation, we take the partial time derivative of the action. But the action comes from integrating the Lagrangian over time, so time seems to just be a dummy variable here and ...
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Why are coordinates and velocities sufficient to completely determine the state and determine the subsequent motion of a mechanical system?
I am a Physics undergraduate, so provide references with your responses.
Landau & Lifshitz write in page one of their mechanics textbook:
If all the co-ordinates and velocities are ...
- 840
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The form of Lagrangian for a free particle
I've just registred here, and I'm very glad that finally I have found such a place for questions.
I have small question about Classical Mechanics, Lagrangian of a free particle. I just read Deriving ...
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Deriving the Lagrangian for a free particle
I'm a newbie in physics. Sorry, if the following questions are dumb. I began reading "Mechanics" by Landau and Lifshitz recently and hit a few roadblocks right away.
Proving that a free ...
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Does locality emerge from (classical) Lagrangian mechanics?
Consider a (classical) system of several interacting particles. Can it be shown that, if the Lagrangian of such a system is Lorenz invariant, there cannot be any space-like influences between the ...
- 34.3k
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Finding Lagrangian of a Spring Pendulum
I'm trying to understand Morin's example of a spring pendulum. What I don't get is his expression for $T$. I can understand the $\dot x^2$ term in the brackets. But I don't understand the $(l + x)^2\...
- 2,251
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Why can't any term which is added to the Lagrangian be written as a total derivative (or divergence)?
All right, I know there must be an elementary proof of this, but I am not sure why I never came across it before.
Adding a total time derivative to the Lagrangian (or a 4D divergence of some 4 ...
- 1,263
4
votes
2
answers
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Derivation of the Lagrangian method using discretized time axis
I'm watching this video lecture by Leonard Susskind of Stanford:
http://www.youtube.com/watch?v=3apIZCpmdls
After some preliminaries, at 34 minutes he jumps into a discretization of the time axis ...
- 2,251
11
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When is the principle of virtual work valid?
The principle of virtual work says that forces of constraint don't do net work under virtual displacements that are consistent with constraints.
Goldstein says something I don't understand. He says ...
- 1,681
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Why can't we ascribe a (possibly velocity dependent) potential to a dissipative force?
Sorry if this is a silly question but I cant get my head around it.
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