Tagged Questions
0
votes
0answers
33 views
Lagrangian with a general constraint [closed]
Can any body help me out to solve this problem?
I am familiar with mechanism of Lagrangian and I can solve some problems with constraints but this one is really hard to solve.
0
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1answer
83 views
A small oscillations of a rod on the cylinder
Let's have the next case.
A rod (with mass $m$, length $L$ and a momentum of inertia $I$) at the initial time is located on a cylinder (with radius $R$) surface so that it's (rod's) center of mass ...
3
votes
3answers
124 views
Virtual differentials approach to Euler-Lagrange equation - necessary?
I'm currently teaching myself intermediate mechanics & am really struggling with the d'Alembert-based virtual differentials derivation for the Euler-Lagrange equation. The whole notion of, and ...
0
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2answers
140 views
Lagrange-Euler equations for a bead moving on a ring
A bead with mass $m$ is free to glide on a ring that rotates about an axis with constant angular velocity. Form the Lagrange-Euler equations for the movement of the bead.
Solution: Let us ...
2
votes
1answer
203 views
Euler-Lagrange Equation
A particle moving towards the origin has initial conditions $x(t=0) = 1$ and $\dot{x}(t=0)=0$
If the Lagrangian is L:=$\frac{m}{2}\dot{x}^2 -\frac{m}{2}ln|x|$
This should satisfy Euler Lagrange ...
1
vote
1answer
153 views
What's the motivation behind the action principle? [closed]
What's the motivation behind the action principle?
Why does the action principle lead to Newtonian law?
If Newton's law of motion is more fundamental so why doesn't one derive Lagrangians and ...
2
votes
3answers
514 views
What exactly are Hamiltonian Mechanics (and Lagrangian mechanics)
What exactly are Hamiltonian Mechanics (and Lagrangian mechanics)?
I want to self-study QM, and I've heard from most people that Hamiltonian mechanics is a prereq. So I wikipedia'd it and the entry ...
0
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0answers
74 views
Describing the movement of the object in a particular situation in Lagrangian way
Suppose there is a object M, (sliding motion) moving by the initial speed $v$ and the initial location $x_0$. Otherwise noted, friction is assumed to be nonexistent. It then meets a circular mold ...
1
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1answer
153 views
Questions regarding solving the Brachistochrone problem using Lagrangian
brachistochrone problem: Suppose that there is a rollercoaster. There is point 1 ($0,0$) and point 2 ($x_2, y_2)$. Point 1 is at the higher place when compared to the point 2, so the rollercoaster ...
6
votes
2answers
214 views
What are the reasons for leaving the dissipative energy term out of the Hamiltonian when writing the Lyapunov function?
I have a problem with one of my study questions for an oral exam:
The Hamiltonian of a nonlinear mechanical system, i.e. the sum of the kinetic and potential energies, is often used as a Lyapunov ...
4
votes
1answer
259 views
Lagrangian dynamics with initial conditions: motion of free particle
I am very new to Lagrangian dynamics so I am trying to get my head around the practical usage. So far on here all I could find were proofs and they did not make much sense to me, especially when time ...
5
votes
1answer
114 views
Elementary derivation of the motion equations for an inverted pendulum on a cart
Consider a cart of mass $M$ constrained to move on the horizontal axis. A massless rod is attached to the midpoint of the cart, having a mass $m$ on its endpoint. See wikipedia for a picture and for a ...
2
votes
1answer
164 views
Do Lagrangian points actually maintain a fixed distance?
I was reading on up Lagrangian points and the restricted three-body problem.
From what I was able to tell, the Lagrangian points are 5 points in a two-body system such that a third body would be ...
3
votes
1answer
304 views
A Question about Virtual Work related to Newton's Third Law
In describing D'Alembert's principle, the lecture note I was provided with states that the total force $\mathbb F_l$ acting on a particle can be taken as,
$$\mathbb F_l=F_l+\sum_mf_{ml}+C_l,$$
...
3
votes
1answer
386 views
When is the principle of virtual work valid?
The principle of virtual work says that forces of constraint don't do net work under virtual displacements that are consistent with constraints.
Goldstein says something I don't understand. He says ...
3
votes
1answer
128 views
Showing constraint is nonholonomic
One example of a nonholonomic constraint is a disk rolling around in the cartesian plane that is constrained to not be slipping.
These leads to the constraint $dx - a \sin\theta d\phi = 0$ and $dy - ...
1
vote
1answer
120 views
Is the number of independent constants of a system equal to the number of degree of freedom of it?
Maybe the question is not very clear myself since I am not a physics major.But can you help me make this question clearer and then give me some comments on it?
I got that this holds in gravitional ...
13
votes
6answers
5k views
What is the difference between Newtonian and Lagrangian mechanics in a nutshell?
What is Lagrangian mechanics, and what's the difference compared to Newtonian mechanics? I'm a mathematician/computer scientist, not a physicist, so I'm kind of looking for something like the ...
2
votes
3answers
337 views
What is the definition of momentum when a mass distribution $\rho(r,t)$ is given?
This question is Edited after recieving comments.
What is the definition of momentum when a mass distribution $\rho(r,t)$ is given?
Assuming a particle as a point mass we know the definition of ...
