Physical Principles & Mathematical Derivation
In a uniform gravitational field with zero air resistance, horizontal velocity vx remains constant while vertical velocity vy accelerates downward at −g, tracing a symmetric Galileo parabola maximized at θ = 45°. Enabling quadratic air drag (Fd = kd·v²) breaks symmetry, steepens descent, and shifts optimal range angle below 45°.
Questions & Concepts
What physical equation governs Projectile Motion Simulator (Parabolic Trajectory & Air Drag)?
R = (v0² × sin(2θ)) / g, H_max = (v0 × sin θ)² / (2g) — In a uniform gravitational field with zero air resistance, horizontal velocity vx remains constant while vertical velocity vy accelerates downward at −g, tracing a symmetric Galileo parabola maximized at θ = 45°. Enabling quadratic air drag (Fd = kd·v²) breaks symmetry, steepens descent, and shifts optimal range angle below 45°.
How are the equations of motion integrated in this simulation?
Nonlinear differential equations are integrated at 240–300 Hz substeps using classical 4th-order Runge-Kutta (RK4) to maintain strict Hamiltonian energy accuracy.