All Questions
11
questions
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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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Is the Kinetic minus potential energy the only type of Lagrangian function? [duplicate]
In Landau-Lifshitz's "Course of Theoretical Physics - Mechanics"
It is told that a lagrangian is a function $\mathcal{L}$ such that the action $S$, defined by:
$$S=\int_{t_0}^{t_1}\mathcal{L}...
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Weird question: elements of eigenvector as kinetic and potential energies
Assume we have $N$ particles each having some potential and kinetic energies. Denote the sum of kinetic energy as $\sum_i T_i = T$ and the sum of potential energy as $\sum_i V_i= V$. This is a closed ...
- 101
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689
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Lagrangian intuition [duplicate]
I am new to lagrangian mechanics and it just baffles me the idea of subtracting potential energy from kinetic energy. Why don't we use kinetic energy alone and the least action path (between two ...
- 105
7
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2
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2k
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Example in motivation for Lagrangian formalism
I started reading Quantum Field Theory for the Gifted Amateur by Lancaster & Blundell, and I have a conceptual question regarding their motivation of the Lagrangian formalism. They start by ...
- 203
3
votes
1
answer
537
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Doubt in the expression of Lagrangian of a system [duplicate]
There is a problem given in Goldstein's Classical Mechanics Chapter-1 as
20. A particle of mass $\,m\,$ moves in one dimension such that it has the Lagrangian
\begin{equation}
L\boldsymbol{=}\...
- 436
7
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2
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3k
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Lagrangian potential for Newtonian gravity
In the Wikipedia site for Lagrangian (field theory) the Lagrangian density for Newtonian gravity is given by
$${\cal L}(\mathbf{x},t) = \frac{1}{2}\rho(\mathbf{x},t)\mathbf{v}^2 -\rho(\mathbf{x},t) \...
- 105
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1
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59
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Does $L=T-V$ still hold when $L$ is NOT time-dependent?
I am aware that the Lagrangian $L=T-V$ where $T$ is the kinetic energy and $V$ is the potential energy when $L$ depends on, for example, $r, \dot{r}, t$. My question is, does this still hold when the ...
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4
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1
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188
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Where does the definition for energy in PDE come from in physics
We defined energy in the context of the wave equation in my PDE class to be
$$
E(t)=\int_{\mathbb{R}^n}\left(u_t^2+[\nabla_{\vec{x}} u]^2\right)d^n\vec{x}
$$
Where $u$ satisfies the wave equation
$$
...
- 286
4
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1
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427
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To derive the relation between work function and potential energy
I'm reading "The variational principles of mechanics- Lanczos",
The author mentions a relation between Work-Function $U(q_1,q_2,\cdots,q_n,\dot q_1,\dot q_2,\cdots,\dot q_n)$ and the potential ...
- 1,028
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2
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Does potential energy always equal kinetic energy?
When I studied physics in junior high and high school, we always took it for granted that potential energy was equal to kinetic energy. In Lagrangian terms, $T = V$at least on average. But I realized ...
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