All Questions
32
questions
2
votes
1
answer
125
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Potential energy and conservation law
I'm preparing for my masters entrance exam on pure mathematics (thought some problems are devoted to classical/lagrangian mechanics). I would be grateful to clarify some basics regarding the ...
- 123
1
vote
0
answers
527
views
Particle in electromagnetic field Lagrangian
Given the two definitions of $\vec E$ and $\vec B$ by scalar potential $\phi$ and vector potential $\vec A$:
$$\vec B=\vec \nabla \times \vec A$$
$$\vec E=-\vec \nabla \phi -\frac 1 c\frac {\partial \...
- 141
2
votes
1
answer
271
views
Lagrangian of a massive particle in an electromagnetic field
I am trying to find the Lagrangian of a massive particle in an electromagnetic field using the Lorentz force: $$ \vec F = q ( \vec E + \vec v \times \vec B)$$ with $$\vec E = - \nabla \phi - \frac{\...
- 43
0
votes
0
answers
118
views
From Lagrangian of Electromagnetic field to the Lorentz force? [duplicate]
The dynamics of a charged particle with velocity $\textbf{v}$ in electromagnetic field is dominated by the Lorentz force
$$\textbf{F} = q(\textbf{E}+{\textbf{v} \times \textbf{B}}), \tag{1}$$
and ...
- 1,757
1
vote
0
answers
215
views
Effective potential in Lagrangian
I have two question related to the steps in equations 3-7 in this paper:
Question 1 They find the effective potential in eq. (5) as the negative of the effective Lagrangian (eq. (3)). I don't see how ...
- 117
0
votes
2
answers
4k
views
Potential energy of an Atwood Machine [closed]
The two weights on the left have equal masses $m$ and are connected by a massless spring of force constant $k$. The weight on the right has mass $M=2m$, and the pulley is massless and frictionless. ...
- 171
4
votes
3
answers
2k
views
Feynman's explanation of virtual work given in his book Feynman's lectures on Physics
In his book Chapter 4 Conservation of Energy, on Gravitational potential energy the discussion goes...
Take now the somewhat more complicated example shown in Fig. 4-6. A rod
or bar, 8 feet long, is ...
1
vote
1
answer
1k
views
Force and energy relation: in case of time dependent force
The equivalent problems are also found in Marion problem 7-22, and other formal classical mechanics textbook. Here what i want to know why instructor solution and some websites gives this kinds of ...
- 3,622
2
votes
2
answers
6k
views
How to calculate the period of the movement from a potential?
I have an assignment, where I have an object moving in 1-D with a given mass and energy, and the potential V(x), and I'm supposed to calculate the period of the movement as a function of the energy
$...
- 69
1
vote
1
answer
1k
views
Potential Energy in modified Atwood Machine
The initial length of the spring is $l_0$.
I need help understanding how the potential energy of this system comes to be. I know the answer:
$$
U = -(m_1-m_2)gx-(m_1+m_2)gy+\frac{1}{2}k(y-l_0)^2+...
- 197
2
votes
1
answer
1k
views
Lagrange equation and a force derivable from a generalized potential
I was reading the solution of this exercise and I have a doubt:
A point particle moves in space under the influence of a force derivable from a generalized potential of the form $$U(r,v) = V(r)+\...
- 175
1
vote
2
answers
2k
views
Pendulum point in polar coordinates for Lagrangian
So I'm really stumped with this. I have a particle in a cone, like pictured. The particle orbits the z axis on the dotted line for $r$.
So knowing that $\alpha$ and $r$ remain constant in this ...
- 111
3
votes
1
answer
2k
views
Finding potential energy of a solid hemisphere on top of another solid hemisphere [closed]
A solid hemisphere with radius $b$ has its flat surface glued to a
horizontal table. Another solid hemisphere with radius $a$ rests on top
of the hemisphere of radius $b$ so that the curved ...
- 111
3
votes
0
answers
182
views
Double pendulum find first integral [closed]
Consider the following situation of a double pendulum in 2D.
We found the moving equations as
$$
\ddot{\theta_1}=-L_1\sin\theta_1 + \frac{m_2}{m_1}\cos\theta_2\sin(\theta_2-\theta_1),\\
\ddot{\theta}...
- 183
3
votes
3
answers
2k
views
Potential energy of an infinitesimal length of elastic rod
I am having an embarrassingly hard time with the derivation for the potential energy of an infinitesimal element of an elastic rod of area $A$. The picture shown below is an element of the rod that ...
- 423