Exact Taylor Projectile Motion
I recently built a physics simulator without air resistance, modeling a body’s motion through a Taylor expansion based on its initial conditions: $$ x(t) = x^{(0)} + t x^{(1)} + \frac{1}{2} t^2 x^{(2)} + \frac{1}{6} t^3 x^{(3)} + \cdots + \frac{t^k}{k!} x^{(k)} $$ where $ x^{(k)} $ represents the $ k $-th derivative of the position vector at time $ t = 0 $. The project mainly focuses on ballistics, hence the name web-ballistics-3d....