All Questions
Tagged with classical-mechanics lagrangian-formalism
251
questions with no upvoted or accepted answers
2
votes
2
answers
108
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How to explain the independence of coordinates from physics aspect and mathmetics aspect?
When I was studying Classical Mechanics, particularly Lagrangian formulation and Hamiltonian formulation. I always wondering how to understand the meaning of independence of parameters used of ...
- 529
2
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0
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57
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What are the extra terms in the generalized momentum regarding the Lagrangian formalism?
In the lectures, we have defined the generalized momentum in the Lagrangian to be:
$$p_i=\frac{\partial L}{\partial\dot q_i}.$$
But with this definition, if we do not make any assumptions about the ...
- 193
2
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0
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117
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Choosing coordinates to solve problems using Lagrangian mechanics
I am trying to obtain the equations of motion using the euler-lagrange equation.
First, let $x$ be the distance of disc R from the wall. Let $y_p$ and $y_q$ be the distance of disc P and disc Q from ...
- 21
2
votes
1
answer
104
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Derivatives of the multipliers appearing in the Euler-Lagrange equation
(This is a crossed post where physical considerations can be helpful.)
Let $\Omega\subset \mathbb{R}^2$ be some simply connected domain and consider the functional
\begin{align}
V\left[u(x,y),v(x,y),w(...
2
votes
1
answer
117
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Do Legendre transformation form a group?
In my classical mechanics class, my professor asked if Legendre transformations form a group, and in my little knowledge about groups, I know that a transformation group consists of a set of ...
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2
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answers
44
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How are conjugate variables in mechanics and stat mech related to duality in convex optimization?
I recently studied duality in optimization where a primal optimization problem can be casted as a dual problem which provides meaningful lower bounds on the primal. There is also a notion of conjugate ...
- 131
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0
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141
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Understanding the Degrees of freedom of a Ballbot
A Ball Balancing Robot is dynamically stable robot capable of omnidirectional motion. It possesses non-holonomic properties and is a special case of underactuated system, classified as a Shape-...
- 71
2
votes
1
answer
209
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Non-Holonomic constraint in rigid body dynamics
I have solved many problems on Holonomic constraint using Lagrange multiplier method but I don't know how to tackle problems on non-Holonomic constraint.
Can anyone help me with the following problem ...
- 33
2
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1
answer
803
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A particle constrained to always move on a surface whose equation is $\sigma (\textbf{r},t)=0$. Show that the particle energy is not conserved
In Goldstein's Classical mechanics question 2.22
Suppose a particle moves in space subject to a conservative potential $V(\textbf{r})$ but is constrained to always move on a surface whose equation is ...
- 173
2
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0
answers
210
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Galileo's Principle of Relativity in Lagrangian Mechanics
Q. Does Galileo's principle of relativity I imply Galileo's principle of relativity II?
Galileo's principle of relativity I: Newton’s equations $\ddot{x} = F(x, \dot{x}, t)$ are invariant under the ...
- 41
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1
answer
245
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How to calculate generalized force $Q_\phi$ with d'Alembert's principle?
The related post was found here Lagrangian formalism application on a particle falling system with air resistance and also Wikipedia's definition on generalized force. Essential
$$\frac{d}{dt}\frac{\...
- 3,256
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161
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Problem understanding something from the variational principle for free particle motion (James Hartle's book, chapter 5)
I am currently studying general relativity from James Hartle's book and I have trouble understanding how he goes to equation (5.60) from equation (5.58). It's about the variational principle for free ...
2
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186
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Lagrangian and convexity
Is it possible to model any physical system with a Lagrangian convex in its velocity variables ?
I am aware that many Lagrangian can model the same system and maybe not all of them are partially ...
2
votes
1
answer
109
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How does derivation of Lagrange equation from d’Alembert principle differ from the derivation of it from principle of least action?
Using d’Alembert principle, one doesn't require any assumption like the one made in other case where particle has to follow the path of least action.
- 21
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333
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How do we get Maupertuis Principle from Hamilton's Principle?
Maupertuis principle says that if we know the initial and final coordinates but not time, the total energy and the fact that energy is conserved, we can choose the "right" path from all mathematically ...
