All Questions
Tagged with calculus classical-mechanics
60
questions
6
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3
answers
1k
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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 ...
Buzz♦
- 16.3k
1
vote
2
answers
127
views
On Landaus&Lifshitz's derivation of the lagrangian of a free particle [duplicate]
I'm reading the first pages of Landaus&Lifshitz's Mechanics tome. I'm looking for some clarification on the derivation of the Lagrange function for the mechanical system composed of a single free ...
- 38.7k
4
votes
1
answer
1k
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Landau's derivation of a free particle's kinetic energy- expansion of a function?
I was reading a bit of Landau and Lifshitz's Mechanics the other day and ran into the following part, where the authors are about to derive the kinetic energy of a free particle. They use the fact ...
- 206k
2
votes
2
answers
825
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Necessary and Sufficient Conditions for an Equilibrium to be Stable
In the 4th section The condition that convection be absent of the book Fluid Mechanics by Landau and Lifshitz, they give the following statement:
For the (mechanical) equilibrium to be stable, it is ...
CommunityBot
- 1
1
vote
1
answer
64
views
Material to Study the Definition, Algebra, and Use of Infinitesimals in Physics [closed]
This is going to be a rather general question about suggestions on best supplementary material to properly explain the use of infinitesimals (or differentials?) for the purposes of integration or ...
- 206k
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 ...
- 194
1
vote
2
answers
119
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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 ...
9
votes
7
answers
2k
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What does it mean to integrate with respect to mass?
I've encountered many integrals that seem to integrate functions of distance with respect to mass, for example, $\int_0^Mr^2dm$ for the moment of inertia of continuous mass distribution.
I'm not sure ...
- 73
1
vote
2
answers
129
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Time derivative of unit velocity vector?
Let's say I have some parametric curve describing the evolution of a particle $\mathbf{r}(t)$. The velocity is $\mathbf{v}(t) = d\mathbf{r}/dt$ of course. I am trying to understand what the expression ...
- 5,068
2
votes
5
answers
261
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Why does $\vec{r}\cdot\dot{\vec{r}}=r\dot{r}$?
Why is $$\vec{r}\cdot\dot{\vec{r}}=r\dot {r}$$ true? Before saying anything, I have seen the proofs using spherical coordinates for $$\dot{\vec {r}}= \dot{r}\vec{u_r}+r\dot{\theta}\vec{u_\theta}+r\sin\...
- 12.4k
1
vote
1
answer
48
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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
votes
1
answer
159
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Recommended physics book(s) that uses calculus and have difficult problems [closed]
What physics book(s) uses calculus and has complex problems (undergrad/olympiad level)?
Context:
I've read "Fundamentals of Physics by Halliday and Resnick" and I found the problems to be ...
- 1
0
votes
2
answers
129
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Does the gradient of potential energy exist independent of coordinates?
Potential energy $U(\vec{r})$ of a conservative force field $\vec{F}$ is defined as a function whose variation between positions $\vec{r}_A$ and $\vec{r}_B$ is the opposite of the work done by the ...
- 12.4k
0
votes
2
answers
63
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Approximation of Small Perturbation [closed]
From Morin's Classical Mechanics, on the chapter of Small Oscillations in Lagrangian Mechanics, he does this approximation on the last equality, I don't understand what happened there.
I get the first ...
- 2,946
0
votes
0
answers
111
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Question on non-holonomic constraints (This is different to the others)
I know there are many posts on non-holonomic constraints and also many on this exact one but I feel that there is still some confusion on it.
"Consider a disk which rolls without slipping across ...
- 206k