N-Body Simulation

Theory Step 1: Particle Characteristics Each particle is treated as a point mass, and each point mass has three intrinsic characteristics: a mass \(m_i\), a position vector \(\vec{r}_i=\left[\begin{array}{ccc}x_i & y_i & z_i\end{array}\right]\), and a velocity vector \(\vec{v}_i=\left[\begin{array}{ccc}u_i & v_i & w_i\end{array}\right]\). Step 2: Force Calculation According to Newton’s law of universal gravitation, given two distinct point masses in space, the gravitational force acting on the objects takes the form: $$F=G\frac{m_1m_2}{r^2}$$...

December 21, 2022 · 2 min

Method of Characteristics

Theory Inline code \(y_t\). Numerical Implementation Normal: $$y_t = \beta_0 + \beta_1 x_t + \epsilon_t$$ see above.

December 19, 2022 · 1 min