All Questions
78
questions
2
votes
2
answers
682
views
Proof of principle of stationary action when the Lagrangian is not $L=T-V$
The principle of stationary action claims that the action $S$ takes a stationary value in a real system, where:
$$S = \int_{t_1}^{t_2} L dt\tag{1}$$
and $L$ is the Lagrangian of the system. It can be ...
- 337
3
votes
1
answer
148
views
What does Thornton and Marion mean by "validity of Lagrange's equations"?
I am a bit confused about the 2nd statement below from Thornton and Marion 7.4:
It is important to realize that the validity of Lagrange's equations requires
the following two conditions:
The forces ...
- 243
0
votes
0
answers
689
views
Lagrangian intuition [duplicate]
I am new to lagrangian mechanics and it just baffles me the idea of subtracting potential energy from kinetic energy. Why don't we use kinetic energy alone and the least action path (between two ...
- 105
1
vote
0
answers
71
views
Verifying the equation of motion, expressions of kinetic energy and potential energy and how to examine whether motion confined to a plane or not [closed]
A particle is moving in space such that it is attracted towards a fixed point and is proportional to the distance from the fixed point. Derive the Lagrangian and Hamiltonian of the system. Examine ...
- 111
4
votes
2
answers
167
views
Classical Mechanics: Relation between general velocity and general potential function for velocity-dependent potential
How is the general force derived from the general potential for a velocity-dependent potential $U = U(q_j,\dot{q_j})$?
$$Q_j=-\frac{\partial U}{\partial q_j}+ \frac{\mathrm{d}}{\mathrm{dt}}(\frac{\...
- 301
7
votes
2
answers
2k
views
Example in motivation for Lagrangian formalism
I started reading Quantum Field Theory for the Gifted Amateur by Lancaster & Blundell, and I have a conceptual question regarding their motivation of the Lagrangian formalism. They start by ...
- 203
1
vote
1
answer
397
views
Monogenic forces vs generalized forces
Wikipedia article under generalized forces says
Also we know that the generalized forces are defined as
How can I derive the first equation from the second for a monogenic system?
https://en....
- 1,270
3
votes
1
answer
537
views
Doubt in the expression of Lagrangian of a system [duplicate]
There is a problem given in Goldstein's Classical Mechanics Chapter-1 as
20. A particle of mass $\,m\,$ moves in one dimension such that it has the Lagrangian
\begin{equation}
L\boldsymbol{=}\...
- 436
0
votes
0
answers
40
views
Motion near the local maximum of potential energy
Particle is moving along the $x$ axis in the field with potential energy $U(x)$. $U(x) $has local maximum at $x=0$, and the total energy of particle is equal to $E=U(0)$.
I'm supposed to find how the ...
- 101
0
votes
1
answer
149
views
Pseudo force and Potential energy
The pseudo force equation is
$$\vec F_p=-2\,m\,(\vec \omega\times \vec v)-m\,(\vec\omega\times (\vec\omega\times \vec R))$$
where $~\vec v=\dot{\vec{R}}$ and $~\vec\omega=\text{const.}$
the pseudo ...
- 12.4k
0
votes
1
answer
148
views
Particle in a cylinder with a spring, sign convention in potential energy (Lagrangian multipliers)
I'm trying to get the force of constraint. The problem I have is when defying the sign of the potential energy using cylindrical coordinates $(\rho,\phi,z)$, what I have is:
$$
V=mgy-\frac{1}{2}k\left(...
- 7
0
votes
1
answer
569
views
Potential energy of a mass bewteen two springs with pendulum hanging [closed]
I need some help with this problem.
A particle of mass $m_1$ hangs from a rod of negligible mass and length $l$, whose support point consists of another particle of mass $m_2$ that moves horizontally ...
- 103
0
votes
0
answers
32
views
Is It Possible to Express all fundamental forces in the form of generalized potentials? [duplicate]
I have Started reading Hamilton's Principle or Principle of Least Action In first course of Undergraduate classical mechanics.
So, I think it becomes easier to apply the Variational principles if ...
- 784
0
votes
1
answer
157
views
Follow-up on "Derivation of Lagrangian of electromagnetic field from Lorentz force"
I have a follow-up on this post. The way I understand it, if one generally has a velocity-dependent potential $U(q, \dot q, t)$, then we can derive/define a generalized force $$Q_k = \frac{d}{dt}\frac{...
user248824
0
votes
3
answers
960
views
Expression for total potential energy in coupled systems
I was reading through applications of Lagrangian mechanics and the case of coupled oscillators. The example provided is the famous two pendula length $l$ mass $m$ hanging from the ceiling connected by ...
- 418