All Questions
13 questions
27
votes
4
answers
13k
views
Hamiltonian, Lagrangian and Newton formalism of mechanics
If my thinking is wrong please let me know. I have little knowledge on beyond-college physics.
For research purposes, I read a few introductions to these three formalisms of classical mechanics [1,2,...
- 8,071
17
votes
5
answers
2k
views
2- and 3-body problems when gravity is not inverse-square
Suppose that gravity did not follow an inverse-square law, but was instead a central force diminishing
as $1/d^p$ for distance separation $d$ and some power $p$.
Two questions:
Presumably the 2-body ...
- 151k
6
votes
1
answer
238
views
Possibly new solution to equal-mass three-body problem; refinement required
(This is a repost of this question from 18 months ago on the main Mathematics SE site, as the response there has been underwhelming, and I thought here would be a better authority. As you can probably ...
- 201
6
votes
0
answers
498
views
“Cohomological equation” in dynamical systems
Let $$\dot{x}=Ax+v_r(x)+v_{r+1}(x)+ \dots$$ with $x \in \mathbb{C}^n$ and $v_r: \mathbb{C}^n \to \mathbb{C}^n$ a homogenous, polynomial function of order $r.$
Then, being able to find a suitable $h$ ...
- 1,514
4
votes
1
answer
334
views
Examples of particle systems with higher-order collisions
In kinetic theory, one often comes across interacting particle systems with a collisional flavour. I'll currently prefer to think about them as systems of ODEs (or SDEs, Jump Processes, $\ldots$), ...
- 801
4
votes
1
answer
368
views
Long wavelength instability: Linear Vs nonlinear phenomenon
I am looking into stability for certain nonlinear PDE on $\mathbb{R}$ around a specific steady solution, $f_0(x)$. The nonlinear Cauchy PDE is given by:
$\dfrac{\partial f(x,t)}{\partial t}=\mathbf{N}...
- 318
3
votes
2
answers
434
views
Classification of Lagrangians with given Euler-Lagrange equations
In (mathematical) physics the equations of motion of a system of particles are often interpreted as Euler-Lagrange equations for appropriate Lagrangian $L=L(x,\dot x,t)$ where $x$ is a collection of ...
- 21.8k
3
votes
1
answer
524
views
Has the von Neumann entropy ever been used in classical mechanics?
After going through an application of the von Neumann entropy(from quantum information theory) to certain problems in computational neuroscience [2], it occurred to me that this entropy might have ...
- 3,871
3
votes
0
answers
127
views
Rigorous stability analysis of infinite dimensional ODEs : How to bound the tails?
My question is about linear stability analysis of dynamical systems obtained by discretizing linear(ized) partial differential equations. Consider,
$\dot{x}=Ax$, where $x$ is the infinite dimensional ...
- 2,281
3
votes
0
answers
79
views
Generalisation of Lyapunov time to stochastic dynamical systems
Might there be useful generalisations of the Lyapunov time to stochastic dynamical systems? In particular, I'm interested in methods for calculating confidence intervals around stochastic analogues of ...
- 3,871
3
votes
0
answers
194
views
Rigid-body in a central field: orbital and attitude motion
Question
I would like to find a nice set of explicit coordinates for the family (parametrised by angular momentum) of reduced systems representing a rigid-body in a central field
in which the orbital ...
1
vote
1
answer
477
views
Partial linearization near a hyperbolic fixed point—Classical scattering
I am currently reading the famous article "Universal Properties of Maps on an Interval"
by Collet, Eckmann and Lanford related to the Feigenbaum–Coullet–Tresser universality.
I am in ...
1
vote
0
answers
108
views
Stability of rigid bodies spinning around $z$-axis under gravity
Consider the problem of a rigid body rotating in 3D space under gravity with one point fixed. I am particularly curious about the equilibrium state where the body is spinning at a constant angular ...
- 807