All Questions
Tagged with classical-mechanics lagrangian-formalism
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What is the physical significance of this generalised potential?
Consider a generalised potential of the form $U=-f\vec{v}\cdot\vec{r}$ where $f$ is a constant. This potential should not contribute any internal forces between particles as
\begin{equation}
\vec{F}=-\...
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Analyzing uniform circular motion with Lagrangian mechanics
Consider swinging a ball around a center via uniform circular motion. The centripetal acceleration is provided by the tension of a rope. Now, is this force a constraint force? If it is, since it is ...
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Degrees of freedom for Constrained Motion
I'm starting to learn about Degrees of freedom, and the idea of 'constrained motion' seems strange to me, surely any particle with a predefined path is 'constrained' in its motion, We also had ...
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How to go from Lagrange equations to d'Alembert's principle?
All sources I know show how to use d'Alembert's principle and/or Hamilton's principles to derive Lagrange equations. It is also common to use d'Alembert's principle to derive Hamilton's principle (see ...
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Decomposing Lagrangian into CM and relative parts with presence of uniform gravitational field
Most problems concerning two-body motion (using Lagrangian methods) often only consider the motion of two particles subject to no external forces. However, the Lagrangian should be decomposable into ...
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Lagrange's equation - thin disk that rolls without slipping on a horizontal plane
The Goldstein book has the following question (1.11):
Consider a uniform thin disk that rolls without slipping on a horizontal plane. A horizontal force is applied to the center of the disk and in a ...
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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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IPhO2014 T1 with Lagrange multipliers
I'm trying to solve IPhO2014 Problem 1 with the method of Lagrange multipliers and I'm facing some problems.
I choose the origin to be at the center of the cylinder, and use three coordinates: $(x, y)...
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Oscillating inverted hemisphere Lagrangian mechanics problem
I am trying to solve a hw problem on Lagrangian mechanics. Here is the problem:
The main issue I am having is setting up the kinetic energy. I don't understand whether the hemisphere has both ...
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Deeper explanation for Principle of Stationary Action [duplicate]
The Principle of Stationary Action (sometimes called Principle of Least Action and other names) is successfully applied in a wide variety of fields in physics. It can often can be be used to derive ...
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Why the choice of Configuration Space in Hamilton's Principle is $(q, \dot{q}, t)$? [closed]
In most physics books I've read, such as Goldstein's Classical Mechanics, the explanation of Hamilton's principle took into consideration the equation (1) known as Action:
$$\displaystyle I = \int_{...
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Is there a proof that a physical system with a *stationary* action principle cannot always be modelled by a *least* action principle?
I'm aware that with Lagrangian mechanics, the path of the system is one that makes the action stationary. I've also read that its possible to find a choice of Lagrangian such that minimization is ...
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Any good resources for Lagrangian and Hamiltonian Dynamics?
I'm taking a course on Lagrangian and Hamiltonian Dynamics, and I would like to find a good book/resource with lots of practice questions and answers on either or both topics.
So far at my university ...
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D'Alembert derivation of Lagrange Equation - why can it use both virtual and normal differentials?
In "Classical Mechanics" by Goldstein and "A Students Guide to Lagrangians and Hamiltonians" by Hamill I noticed that both the virtual displacement derivatives and the normal displacement derivatives ...
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Units for the Calculus of Variations [duplicate]
Just a quick question regarding the units for a quantity. I just started reading a QFT textbook, and it starts out with a little bit of Calculus of Variations. Specifically, there is a result that ...
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