All Questions
50
questions
0
votes
1
answer
87
views
Help with understanding virtual displacement in Lagrangian
I know that these screen shots are not nice but I have a simple question buried in a lot of information
My question
Why can't we just repeat what they did with equation (7.132) to equation (7.140) ...
- 283
0
votes
2
answers
530
views
Why is derivative of Lagrangian with respect to generalized position and velocity equal to this?
I'm currently studying Lagrangian mechanics, and in the process, I've met the following equations in a couple of proofs.
$$
\frac{\partial \mathcal{L}}{\partial q_i} = \dot p_i
$$
$$
\frac{\partial \...
user334560
0
votes
0
answers
95
views
Conjugate momentum vs translation generator with non-standard kinetic term
I am reading this paper and for equation (2.5) (associated with the Lagrangian in eq 2.1) there is the claim that for a Lagrangian $L(\varphi,A,\dot{\varphi},\dot{A})$ containing an extra non-standard ...
3
votes
5
answers
370
views
Axiomatising classical mechanics to arrive at the principle of stationary action - what are the fundamental definitions of momentum, etc.?
$\newcommand{\d}{\mathrm{d}}\newcommand{\l}{\mathcal{L}}$Throughout all my study of physics, it has never been clear what is a definition, what is an axiom, what is a law and what is a proof in ...
- 221
3
votes
0
answers
121
views
Intuitive explanation on why velocity = 0 for a inverted pendulum on a wheel system
I believe I have solved below problem. I am not looking for help on problem-solving per se. I am just looking for an intuitive explanation.
Problem statement: wheel mass = $m_1$, even mass rod BC mass ...
- 131
1
vote
1
answer
108
views
Geometric meaning of conjugate momentum
Let's say I have a free particle moving in an $n$-dimensional Manifold $M$. There is a tangent space $TM$ associated with all possible infinitesimal motions of a particle at each point in this ...
- 137
2
votes
2
answers
156
views
How to derive the fact that $p\sim d/dx$ and $H\sim d/dt$ from classical mechanics?
I am trying to understand Noether's conserved quantities to shifts in time and or position. I have seen the derivation of the operators for Schrodinger's equation but not for classical mechanics.
Is ...
- 381
0
votes
0
answers
124
views
Lagrangian and Friction
How does lagrangian mechanics explain loss of momentum conservation in presence of friction?
My try is this:
The lagrange equation would then include a generalized force term $Q_i$:
$$\frac{d}{dt}\...
- 132
2
votes
2
answers
161
views
Conjugate momentum notation
I was reading Peter Mann's Lagrangian & Hamiltonian Dynamics, and I found this equation (page 115):
$$p_i := \frac{\partial L}{\partial \dot{q}^i}$$
where L is the Lagrangian. I understand this is ...
- 41
0
votes
1
answer
320
views
Gauge ivariance and canonical versus kinetic momenta for a charged particle in an EM field
I all, I am struggling to grasp the notion of gauge invariant when talking about an object like the canonical momenta $\frac{\partial L}{\partial \dot{q}_i}$ or kinetic momenta $m\dot{q}_i$.
I am very ...
- 1,031
3
votes
1
answer
151
views
Reducing the degrees of freedom of a Lagrangian in a spherical potential by using integrals of motion [duplicate]
I'm sure I've made a silly mistake here, so I would be very grateful if someone could help me clear it up! Here is my reasoning:
The Lagrangian in a spherical potential is
$$
\mathcal{L}=\frac{m\...
- 2,157
1
vote
2
answers
202
views
Does the conservation of $\frac{\partial L}{\partial\dot{q}_i}$ necessarily require $q_i$ to be cyclic?
If a generalized coordinate $q_i$ is cyclic, the conjugate momentum $p_i=\frac{\partial L}{\partial\dot{q}_i}$ is conserved.
Is the converse also true? To state more explicitly, if a conjugate ...
- 11.8k
0
votes
1
answer
328
views
Difference between kinematic momentum and conjugated momentum in purely mechanical setup
I don't know much about physics, but I wanted to understand what was the difference between the "kinematic momentum" and the conjugated momentum. As I understand it, kinematic momentum is mass times ...
- 111
1
vote
2
answers
352
views
Ambiguity in d'Alembert's principle
It seems to me that many different momenta $\dot{\bf p}_j $ can satisfy d'Alembert's principle:
$$\tag{1} \sum_{j=1}^N ( {\bf F}_j^{(a)} - \dot{\bf p}_j ) \cdot \delta {\bf r}_j~=~0 $$
in a ...
- 121
2
votes
2
answers
2k
views
Defining generalized momentum in terms of kinetic energy versus a Lagrangian
Reputable authors (e.g., Bergmann, Wells, Susskind) define generalized momentum using the Lagrangian $L$ as $$p_{i}\equiv\frac{\partial L}{\partial\dot{q}^{i}}.\tag{1}$$
Joos and Freeman define ...
- 2,015