All Questions
5
questions with no upvoted or accepted answers
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Does the additivity property of Integrals of motion and Lagrangians valid in all situations?
I would like to know if the additivity property of an integral (constant) of motion valid in all situations ? It works for energy but does it work for all other integrals of motion in all kinds of ...
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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
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What is the physical interpretation of a Lagrangian with $\dot{x}^4$?
Among the exercises in the first chapter of Goldstein's book "Classical Mechanics", it appears the lagrangian
$$
L\left(x,\frac{dx}{dt}\right) = \frac{m^2}{12}\left(\frac{dx}{dt}\right)^4 + m\left(\...
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Lagrange Equation - Basics
The basic equation of Lagrange is given by,
$$\frac{\mathrm d}{\mathrm dt} \frac{\partial L}{\partial \dot{q_j}} - \frac{\partial L}{\partial q_j} = Q_j \tag{1}$$
where $T$ is the kinetic energy, $V$ ...
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Is there a straightforward simplified proof of energy conservation from time translation symmetry?
Electric charge conservation is easily proven from electric potential gauge symmetry, as follows:
The potential energy of an electric charge is proportional to the electric potential at its location.
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