# Questions tagged [classical-mechanics]

For questions on classical mechanics from a mathematical standpoint. This tag should not be the sole tag on a question.

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### Proof of Identity for Lagrangians

My textbook states (in a derivation of the Euler-Lagrange equation) the following which I would like to understand: \begin{equation*} S[\bar{x}+\delta x] =\int_{t_a}^{t_b} L(\dot{x}+\delta \dot{x}, x+\...
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### How to prove the brachistochrone to be Isochronous

When I was reading the calculus of Variations chapter in Classical Mechanics by John R. Taylor, he mentioned that cart rolling back and forth on cycloid-shaped track are exactly isochronous (period ...
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### Prove that if air resistance is proportional to velocity, then impact speed will be lower than projection speed.

The full question is: A particle of mass m is projected vertically upwards through a resistive medium with initial speed $u$. It experiences a resistive force of $mkv$. and a weight force $mg$. When ...
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### unknown manipulation to deal with variation and obtain energy balance equation?

I'm studying a paper relevant to using d'Alembert's principle to describe the motion of fluid. The authors shows an interesting manipulation to obtain energy balance equation, which makes me confused. ...
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### How to model a ball moving on the graph of $z=f(x,y)$ by gravity action? [closed]

I want to model the movement of a ball constrained on the graph $z = f(x, y)$ (for instance $z = \cos(x^2 + y^2)$ by the action of gravity only (no friction or drag and no air resistance) do you have ...
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1 vote
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### Using trigonmetry to compute valid configuration(s) of a 2D four bar linkage given a specific constraint

I'm trying to find an analytical solution to an inverse kinematics problem for a software project, and after simplifying things as much as possible I've come up with the following problem statement. ...
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### Modelling a differential equation for a practical problem in fluid mechanics

I have been working on modeling the time taken to empty a cylindrical tank with a sealed top using a moving lid. The lid, in the form of a disk, moves down as the water level decreases. The discharge ...
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### Why only "small" variation considered in the formulation of Euler Lagrange equations?

For the Euler Lagrange equation formulation, they only use a "small" variation $\varepsilon$ for \begin{equation} y(x,\varepsilon) = y(x) + \varepsilon\eta(x) \end{equation} where $y(x)$ is ...