All Questions
6
questions with no upvoted or accepted answers
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
3
votes
0
answers
830
views
Gauge freedom in Lagrangian corresponds to canonical transformation of Hamiltonian
I want to show that the gauge transformation
$$L(q,\dot{q},t)\mapsto L^\prime(q,\dot{q},t):=L(q,\dot{q},t)+\frac{d}{dt}f(q, t)$$
corresponds to a canonical transformation of the Hamiltonian $H(p, q, ...
- 1,187
2
votes
0
answers
57
views
What are the extra terms in the generalized momentum regarding the Lagrangian formalism?
In the lectures, we have defined the generalized momentum in the Lagrangian to be:
$$p_i=\frac{\partial L}{\partial\dot q_i}.$$
But with this definition, if we do not make any assumptions about the ...
- 193
1
vote
1
answer
51
views
Lagrange momentum for position change
After the tremendous help from @hft on my previous question, after thinking, new question popped up.
I want to compare how things behave when we do: $\frac{\partial S}{\partial t_2}$ and $\frac{\...
- 525
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 ...
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