All Questions
Tagged with classical-mechanics differentiation
123
questions
6
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3
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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 ...
1
vote
3
answers
102
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The conservative force [closed]
I read about the definition of the curl.
It's the measure of the rotation of the vector field around a specific point
I understand this, but I would like to know what does the "curl of the ...
- 11
1
vote
2
answers
99
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Why must a constraint force be normal?
If we impose that a particle follows a holonomic constraint, so that it always remains on a surface defined by some function $f(x_1,x_2,x_3)=0$ with $f:\mathbb{R^3}\rightarrow\mathbb{R}$, we get a ...
- 101
1
vote
1
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64
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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 ...
0
votes
1
answer
76
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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 ...
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0
votes
1
answer
75
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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
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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
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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}{\...
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2
votes
1
answer
89
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Time derivative of a "general" vector $\vec A$ in an accelerating frame: what about e.g. velocity $\vec v$?
According to Morin "Classical Mechanics" (Section 10.1, page 459), the derivative of a general vector $\vec A$ in an accelerating frame may be given as
$$\frac{d\vec A}{dt}=\frac{\delta \vec ...
- 23
2
votes
5
answers
261
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Why does $\vec{r}\cdot\dot{\vec{r}}=r\dot{r}$?
Why is $$\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\...
- 69
2
votes
6
answers
236
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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
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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 ...
- 525
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
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 ...
- 577
1
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2
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221
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Why the $\Delta$ in the definition of pressure? (fluid mechanics)
I'm an engineering student (first year) studying Physics 1 (now an introduction to fluid mechanics).
Q1
In my physics textbook, the "medium pressure" is defined as:
$$p_m = \frac{\Delta F_{\...
- 141