All Questions
Tagged with nonlinear-dynamics mathematical-physics
8
questions
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71
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Mathematical theory of plasma
I am working on a heavily mathematically project about plasma. In particular, I want to find references that treat the problem from microscopic models that include relativistic and magnetic effects (...
- 113
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24
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How to know if a set of equations are Lorentz Invariant Spinors
I'm currently busy with a course in QFT and am completely baffled by Spinors. In particular there are two parts, that while I mostly understand the theory, struggle to show mathematically (especially ...
- 39
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1
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597
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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
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146
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How can I find the fixed points of this Duffing oscillator differential equation?
The problem is to find the fixed points for the equation:
$$\ddot{x}+ \dot{x}- x + ax^3=b \cos(ct)$$
where $a,b$ and $c$ are constants.
The Duffing oscillator is a 2nd order differential equation and ...
2
votes
0
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51
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Very hard quasilinear PDE
I have the following PDE in two dimensions
$$
2\partial_x\partial_y\sqrt{1-u^2}+\left(\partial^2_x-\partial^2_y \right)u=0,
$$
with $u=u(x,y)$ on some domain of the plane. Now, numerically I can ...
- 165
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21
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Interpretation about the exchange of energy among oscillators
I'm studying Hamiltonian system and in particular the role of frequencies in these systems. What I want to understand is about the physic interpretation of some definition.
Considerer a Hamiltonian ...
1
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2
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2k
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Partial differential equations that involve an infinite "continuum" of variables: "Each point in space contributes additional degrees of freedom"?
Page 11, Nonlinear Dynamics and Chaos, by Strogatz, says the following:
This is the domain of classical applied mathematics and mathematical physics where the linear partial differential equations ...
- 4,322
3
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1
answer
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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