All Questions
Tagged with nonlinear-dynamics physics
10
questions
1
vote
0
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35
views
How to accurately average a function with a nonlinear response?
I am a physics PhD student working in optics and I have a bit of a weird problem that I am trying to sort out and I'm hoping you math folks can help me with.
Without boring you with the experimental ...
4
votes
0
answers
170
views
Dynamics of a sliding cube on the $XY$ and $YZ$ planes
A cube with side length $a$, is initially placed with one vertex at the origin, and its faces parallel to the coordinate planes ($XY, XZ, YZ$) and totally lying in the first octant. Then its rotated ...
- 24.4k
0
votes
1
answer
597
views
Dimensionless form of the ODE for a simple pendulum with forcing and damping
I'm tasked with analysing the behaviour of a simple pendulum with driving and damping, which has the equation of motion:
$$mL^{2}\ddot{\theta} + k\dot{\theta} + mgL\sin{\theta} = FL\cos{\Omega}t$$
For ...
- 15
0
votes
2
answers
173
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Understanding Uniqueness of solutions of differential equations - nonlinear ODEs - pendulum example
Understanding Uniqueness of solutions of differential equations - nonlinear ODEs - pendulum example
I am trying to understand If the nonlinear ODE of the classical equation for the pendulum with ...
- 1,534
5
votes
0
answers
221
views
What are the solutions for $y(t)\cdot\left(y'(t) + a\right)=-b\sin(t)$?
What are the solutions for $y(t)\cdot\left(y'(t) + a\right)=-b\sin(t)$?
It could be proben that there exists some solutions?
Are these solutions unique?
and obviously, which are these solutions? (...
- 1,534
3
votes
1
answer
150
views
It is possible for a scalar finite-duration continuous system to achieve an infinite speed (in finite-time)? How if true? Why not if false?
It is possible for a scalar finite-duration continuous system to achieve an infinite speed (in finite-time)? How if it true? Why not if it false? (Please read first the restrictions of the system I am ...
- 1,534
0
votes
1
answer
105
views
Tilting a mass suspended on 2 springs
I was trying to model the following problem:
There is a solid brick shaped body, with center of mass $(x,y,z)$. We put this body onto 2 springs. For making the problem easier, we cut out the slice ...
1
vote
1
answer
34
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Continuous dependence of duffing oscillator solution on forcing term
Consider the Duffing oscillator $\ddot{x} + 2 \gamma \rho \dot{x} + \rho^2 (\dot{x} + \alpha x^3) = F(t)$ for some forcing term $F(t)$. Are there any results that state that $x$ depends continuously ...
- 3,993
1
vote
1
answer
33
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A particle falling in a resisting medium. Solution to differential eqn of motion.
The particle is falling down, and $x$ is measured in down direction.
$$x''=g-kv^4 \\ \implies\quad v\frac{dv}{dx}=g-kv^4$$
Solving this I get $$\frac{1}{4\sqrt{gk}}\log\bigg(\frac{\sqrt k v^2-\sqrt ...
- 4,711
3
votes
1
answer
84
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How to find out the critical angle of a ball separating the circle?
Question: Let function $x:\mathbf R_+\to[0,2\pi]$ satisfying the second-order nonlinear ODE
\begin{equation}
\left\{
\begin{aligned}
\ddot x(t) &= \sin x(t)-\cos x(t)+{\dot x(t)}^2, \quad t>0;...
- 1,972