Questions tagged [classical-mechanics]

Question 1

I posted this question on physics stack exchange, but I did not get any answer. However, since the topic is clearly very mathematical, I think that it may be appropiate to post it here as well: I am ...

Question 2

Let us consider a Lagrangian system for which the equations of motion come from Hamilton's principle and are such that the control variable $\tau$ equals the equations of motion of a free system, ...

Question 3

Let $u=u_i e_i$ be the displacement field of a continuum body. Then the displacement gradient tensor H based on classical formulation is given by $H=\nabla u = u_{i,j}\, e_i \otimes e_j$, where $\...

Question 4

Here it is shown that (for a "suitable" mathematical definition of fairness) there are no fair $n$-sides die with odd $n$. The question originated with fairness being defined as, among other,...

Question 5

Consider a classical BVP governed by linear elasticity $$ \begin{align*} -\nabla \cdot \boldsymbol{\sigma} = \boldsymbol{b} & \quad \textrm{in} \nobreakspace \nobreakspace \Omega \subset \...

Question 6

Suppose $n$ identical masses (each with mass $m$) lie on a friction-less surface and are connected by springs (each with spring constant $k$ and equilibrium length $a$). Let the positions of the ...

Question 7

In mechanical engineering, there are many designs of a CVT(Continuously Variable Transmissions) that is able to change gear ratio continuously, but all of them are unsatisfactory for some reason. ...

Question 8

I'm tying to find where I went Wrong in my efforts to solve problem 6.1 in Taylor’s book on classical mechanics. Using spherical polar coordinates $(r,\theta,\phi)$, show that the length of a path ...

Question 9

Background. I am working through "Mechanics and Symmetry" by Marsden and Ratiu. In Ch. 3.2, they derive the Klein-Gordon equation using a Hamiltonian of the form $$H(\varphi,\pi)=\int_{\...

Question 10

When is $W(A) = p(|A|)$ a polyconvex function, where $p$ is a polynomial and |A| is the Frobenius norm of the matrix $A$? A sufficient condition: because $|A|$ is convex in the entries of $A$, then $W$...

Question 11

How can we prove the following theorem? Theorem: If $\oplus : R^3 \times R^3 \to R^3$ satisfies: (i) $u \parallel v \implies u \oplus v = u+v$ (ii) $u \oplus v = v \oplus u$ (iii) $u \oplus (v \oplus ...

Question 12

Having started to read Giaquinta/Hildebrandt "Calculus of Variations I", 2 ed. 2004, in order to get a better mathematical foundation for my understanding of the Hamilton principle of least ...

Question 13

Consider a planar Hamiltonian system with Hamiltonian $H(x,y)$, i.e. a system given by $$x^\prime (t) = \frac{\partial H}{\partial y}$$ $$y^\prime(t) = - \frac{\partial H}{\partial x}. $$ Suppose $\...

Question 14

I'm using Goldstein's Classical Mechanics 3rd Ed. In Section 4.9 - Rate of Change of a Vector he derives the components of the angular velocity vector for the rate of vector change transformation ...

Question 15

The number of revolutions per second (rps) of a flywheel slowing down is given in terms of time in the following table: Time (s) Revolutions/second 0 360 30 351 60 324 90 279 120 216 150 135 Find the ...

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Questions tagged [classical-mechanics]

Interpretation and intuition on symplectic reduction

Are the motion equations of an optimal control problem geodesics on a manifold?

Strain Tensor Based on Clifford Algebra

Probability of rolling a specified face for Archimedean solids

How do concentrated (nodal) forces manifest in the weak form of the linear elasticity pde?

Coupled Oscillators or "Springs and Masses" (question about sum of binomial coefficients and a reference request)

Can it be proven that CVT(Continuously Variable Transmissions) are impossible using only smooth rigid bodies?

Geodesics on spheres (from Taylor’s classical mechanics) [duplicate]

Klein Gordon equation using the Hamiltonian Formalism

When is a polynomial in |A| polyconvex?

Sufficient properties of vector addition?

Computing the first variation of a variational integral

Period of Periodic Solutions to Hamiltonian System in Plane

How can I derive angular velocity components using Euler angle parameters & purely using the Euler rotational matrices?

Deriving a quadratic function from a table of values

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