All Questions
Tagged with classical-mechanics lagrangian-formalism
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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:
$$\displaystyle I = \int_{...
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Is there a proof that a physical system with a *stationary* action principle cannot always be modelled by a *least* action principle?
I'm aware that with Lagrangian mechanics, the path of the system is one that makes the action stationary. I've also read that its possible to find a choice of Lagrangian such that minimization is ...
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Units for the Calculus of Variations [duplicate]
Just a quick question regarding the units for a quantity. I just started reading a QFT textbook, and it starts out with a little bit of Calculus of Variations. Specifically, there is a result that ...
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Changing variables from $\dot{q}$ to $p$ in Lagrangian instead of Legendre Transformation
This question is motivated by a perceived incompleteness in the responses to this question, which asks why we can't just substitute $\dot{q}(p)$ into $L(q,\dot{q})$ to convert it to $L(q,p)$, which ...
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Directly integrating the Lagrangian for a simple harmonic oscillator
I've just started studying Lagrangian mechanics and am wrestling with the concept of "action". In the case of a simple harmonic oscillator where $x(t)$ is the position of the mass, I ...
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Why do we multiply the Euler-Lagrange equations by negative one?
As I've learned classical mechanics from different sources, I've seen both
$$\frac{d}{dt} \left( \frac{\partial L}{\partial \dot{q}_k} \right) - \frac{\partial L}{\partial q_k} = 0,$$
and
$$\frac{\...
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Arc length between configurations in the "mass distance"
In classical Lagrangian mechanics, the mass $M$ is a Riemannian metric on the configuration space $Q$.
Does the "arc length" of a path $\gamma : [0, 1] \to Q$,
$$
\int_0^1 {\lVert{\gamma'(t)}...
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How would one use Lagrangian mechanics to obtain equations of motion for a conical pendulum? [closed]
I've defined the origin as the center of rotation for the particle on the pendulum. Then:
$$ x = r\cos{\theta} $$ $$ y = r\sin{\theta} $$ $$z = 0$$
From here, the potential energy is $V = 0$ since $z =...
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Holonomic constraints as a limit of the motion under potential
In Mathematical Methods of Classical Mechanics, Arnold states the following theorem without proof in pages 75-76:
Let $\gamma$ be a smooth plane curve, and let $q_1, q_2$ be local coordinates where
$...
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Regarding varying the coefficients of constraints in the pre-extended Hamiltonian in Dirac method
consider the following variational principle:
when we vary $p$ and $q$ independently to find the equations of motion, why aren't we explicitly varying the Coeff $u$ which are clearly functions of $p$ ...
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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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