ODEs&Chaos

Posted on November 9, 2024November 9, 2024default

齐次微分方程与混沌理论

Basics

Integral curves

If an ODE $\frac{dy}{dx}=f(x,y)$ has solution $y=\phi(x)$ We call curve $y=\phi(x)$ the integral curve.

An example for equation labeling and referring

(1) $\begin{equation*}$\frac{dy}{dx}$\end{equation*}$

as mentioned in 1

Textbook for ODE learning

Find this website of the book {Introduction to Differential Equations}
Currently following the impulse differential equations and laplace transform {Link}

A 1-D balldrop simulator for fun

(2) $\begin{align*}\frac{d^2 y}{dt^2} &= -mg\\\frac{d^2 y}{dt^2} &= -g \\\frac{dv}{dt} &= -g \\v(t) &= v_0 - gt \\y(t) &= y_0 + v_0 t - \frac{1}{2}gt^2 \\\end{align*}$

Shifts into Collision Phase

(3) $\begin{equation*}v_{\text{after}} = -e \cdot v_{\text{before}}\end{equation*}$

Basics

Integral curves

An example for equation labeling and referring

Textbook for ODE learning

A 1-D balldrop simulator for fun

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