All Questions
55
questions
6
votes
3
answers
1k
views
In equation (3) from lecture 7 in Leonard Susskind’s ‘Classical Mechanics’, should the derivatives be partial?
Here are the equations. ($V$ represents a potential function and $p$ represents momentum.)
$$V(q_1,q_2) = V(aq_1 - bq_2)$$
$$\dot{p}_1 = -aV'(aq_1 - bq_2)$$
$$\dot{p}_2 = +bV'(aq_1 - bq_2)$$
Should ...
0
votes
1
answer
76
views
In Lagrangian mechanics, do we need to filter out impossible solutions after solving?
The principle behind Lagrangian mechanics is that the true path is one that makes the action stationary. Of course, there are many absurd paths that are not physically realizable as paths. For ...
- 50.1k
0
votes
1
answer
75
views
Derivation of lagrange equation in classical mechanics
I'm currently working on classical mechanics and I am stuck in a part of the derivation of the lagrange equation with generalized coordinates. I just cant figure it out and don't know if it's just ...
- 41
4
votes
4
answers
245
views
Variation of a function
I'm studying calculus of variations and Lagrangian mechanics and i don't understand something about the variational operator
Let's say for example that i got a Lagrangian $L [x(t), \dot{x}(t), t] $ ...
- 309
1
vote
1
answer
54
views
Sufficient condition for conservation of conjugate momentum
Is the following statement true?
If $\frac{\partial \dot{q}}{\partial q}=0$, then the conjugate momentum $p_q$ is conserved.
We know that conjugate momentum of $q$ is conserved if $\frac{\partial L}{\...
- 41
2
votes
6
answers
236
views
Lagrangian - How can we differentiate with respect to time if $v$ not a function of time?
In the Lagrangian itself, we know that $v$ and $q$ don't depend on $t$ (i.e - they are not functions of $t$ - i.e., $L(q,v,t)$ is a state function.)
Imagine $L = \frac{1}{2}mv^2 - mgq$
Euler-Lagrange ...
- 525
1
vote
2
answers
119
views
Lagrangian total time derivative - continues second-order differential
In the lagrangian, adding total time derivative doesn't change equation of motion.
$$L' = L + \frac{d}{dt}f(q,t).$$
After playing with it, I realize that this is only true if the $f(q,t)$ function has ...
- 525
1
vote
1
answer
48
views
Lagrangian for 2 inertial frames where only Speed is different by small amount
In Landau & Liftshitz’s book p.5, they go ahead and writes down lagrangians for 2 different inertial frames. They say that Lagrangian is a function of $v^2$.
So in one frame, we got $L(v^2)$.
In ...
- 525
1
vote
1
answer
113
views
Is the order of ordinary derivatives interchangeable in classical mechanics?
I am having trouble with a term that arises in a physics equation (deriving the Lagrange equation for one particle in one generalized coordinate, $q$, dimension from one Cartesian direction, $x$).
My ...
- 111
0
votes
0
answers
71
views
Deriving Euler-Lagrange equation [duplicate]
I have derive the Euler-Lagrange equation which is equation (2) for a condition in which generalised velocity is independent on the generalised coordinate but when generalised velocity is dependent on ...
2
votes
1
answer
610
views
Proof that the Euler-Lagrange equations hold in any set of coordinates if they hold in one
This is a question about a specific proof presented in the book Introduction to Classical Mechanics by David Morin. I have highlighted the relevant portion in the picture below.
In the remark, he ...
anon
0
votes
1
answer
88
views
Step in derivation of Lagrangian mechanics
There is a step in expressing the momentum in terms of general coordinates that confuses me (Link)
\begin{equation}
\left(\sum_{i}^{n} m_{i} \ddot{\mathbf{r}}_{i} \cdot \frac{\partial \mathbf{r}_{i}}{\...
- 335
1
vote
1
answer
56
views
Energy change under point transformation
How do the energy and generalized momenta change under the following
coordinate
transformation $$q= f(Q,t).$$
The new momenta: $$P = \partial L / \partial \dot Q = \partial L / \partial \dot q\times ...
- 980
3
votes
2
answers
146
views
How to prove that $ \delta \frac{dq_i}{dt} = \frac{d \delta q_i}{dt} $? [duplicate]
During the proof of least action principle my prof used the equation $ \delta \frac{dx}{dt} = \frac{d \delta x}{dt} $. We were not proved this equality. I was curious to know why this is true so I ...
1
vote
2
answers
2k
views
Derivation of Lagrange's equation form d'Alembert's Principle
Im studying Mechanics form Goldstein. I cross this equation in "Derivation of Lagranges equation from d'Alembert's Principle",section 1.4. I have two questions from this derivation.
The ...
user310684