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Questions tagged [classical-mechanics]

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

Wikipedia says:

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. Besides this, many specializations within the subject deal with gases, liquids, solids, and other specific sub-topics. Classical mechanics provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light.

For questions on classical mechanics from a mathematical standpoint. This tag should not be the sole tag on a question. Examples of other tags that might accompany this include , , and .

2097 questions
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Why don't we differentiate velocity wrt position in the Lagrangian?

In Analytic Mechanics, the Lagrangian is taken to be a function of $x$ and $\dot{x}$, where $x$ stands for position and is a function of time and $\dot{x}$ is its derivative wrt time. To set my question, lets consider motion of a particle along a…
mech_love_not_war
  • 199
11
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2 answers

How does energy conservation follow from Newton's second law?

Question : Show in the one-dimensional case, how for potential forces $F(x) = \dfrac{−dV (x)}{dx}$, energy conservation follows from Newton’s 2nd law From Newton's second law we know $$F=ma=m\ddot{x}$$ How do we derive the conservation of energy…
Mr Croutini
  • 1,158
6
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2 answers

Rigid bodies: proof of existence of internal forces that preserve the distances

I am new to Physics and I have a pure Math background. I am currently studying mechanics and I have the following question regarding rigid bodies. I am posting here the 2D version of the question. If anyone is aware of the answer for the general 3D…
Plemath
  • 439
5
votes
0 answers

Angular momentum cylindrical coördinates

From "Classical Mechanics" - Taylor, problem 3.30 Consider a rigid body rotating with angular velocity $\omega$ about a fixed axix. (You could think of a door rotating about the axis defined by its hinges.) Take the axis of rotation to be the…
dietervdf
  • 4,524
5
votes
2 answers

Finding where a ball loses contact with an exponentialy modled hill given there is no friction.

I have an answer to the following question, but I have no easy way to verify it and would like some feedback, I'll go through my whole process. Imagine a perfectly smooth hill moddled as a $y = -e^x$ curve. We want to study the movement of an…
Bruno Mompeán
  • 51
5
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4 answers

Motion of a body given acceleration as a function of velocity

I'm having trouble figuring this out. I'm trying to determine the final time and final velocity for the motion of a vehicle over a given distance along a straight line. $t$ is time $v$ is velocity $a$ is acceleration $r$ is displacement $m$ and $c$…
Jack
  • 153
5
votes
1 answer

What if the Euler Lagrange equation yields a 'trivial' answer

The example I'm doing gives an equation $$L(y, y') = \frac{y'}{y}$$ then $$\frac{\partial L}{\partial y} = -\frac{y'}{y^2}$$ and $$\frac{\partial L}{\partial y'} = \frac{1}{y}$$ ... $$\frac{d}{dx}\frac{\partial L}{\partial y'} =…
Rawb
  • 443
5
votes
0 answers

How does one calculate a re-bounce sling shot trajectory such a Juno?

looking at this https://i.stack.imgur.com/aoGbU.gif What text book would allow one to calculate such things? DE books in university certainly had nothing that could be of use with such calculations. how does one even knows that when such…
jimjim
  • 9,675
5
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1 answer

Mathematical prediction of synchronizing multiple cams.

I am not a mathematician so be gentle with me but what kind of math equations (or what field of mathematics) would be needed for the following: I have designs for an old-style mechanical device I am creating with a complex set of cams -- a total of…
O.M.Y.
  • 255
5
votes
3 answers

Harmonic oscillator with squared damping term

Does a solution exist for a harmonic oscillator with a squared damping term? $$m\ddot{u}+c\dot{u}^2+ku=0$$
ben
  • 2,155
4
votes
1 answer

Quadratic has 2 solutions but only one is correct. Can't find the reason.

A car travels in a straight line from A to B, a distance of ${12}$ km, taking 552 seconds. The car starts from rest at A and accelerates for ${T_1}$ s at 0.3 $m s^{-2}$ , reaching a speed of V $m s^{−1}$ . The car then continues to move…
842Mono
  • 375
4
votes
1 answer

Configuration space of three points in $\mathbb{R^{3}}$

If $X,Y,Z$ are the distances between three points in $\mathbb{R}^{3}$ such that $X,Y,Z$ satisfy the triangle inequality. What will be the configuration space of the three points, given the translation symmetry (fix one point at origin). Thanks
J Verma
  • 477
4
votes
0 answers

Noether's theorem on Hamiltonian of fluid mechanics

Noether's theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law (from wikipedia https://en.wikipedia.org/wiki/Noether%27s_theorem). Then how is the conservation of mass, momentum…
sam
  • 459
4
votes
1 answer

Show that the angular momentum is conserved (Noether)

It is the first time I get in touch with classical mechanics and this stuff... Suppose a mechanical system has $n$ degrees of freedom described by coordinated $q\in V\subset\mathbb{R}^n$, set $v=\dot{q}$. In the situation of particles under the…
M. Meyer
  • 639
4
votes
2 answers

Classical Mechanics Question

A toboggan travels along the path ABC shown in the diagram. The path lies in a vertical plane, and consists of two circular arcs $AB$ and $BC$. The line ABC is horizontal and there is no friction between the toboggan and the snow. Air resistance is…
user140161
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