MATLAB Simulation of Projectile Motion with Inelastic Collision

Projectile motion is a classic two-dimensional physics problem where an object moves under gravitational influence without air resistance. MATLAB provides an effective platform to simulate this process and incorporate inelastic collision characteristics.

Simulation approach:

Initial Conditions Setup Define the object's initial position, initial velocity, and launch angle. Typically using the horizontal plane as reference, set initial height and horizontal velocity components. In MATLAB code, this involves declaring variables like `initial_height`, `v0` (initial velocity), and `theta` (launch angle) using basic assignment operations.

Motion Equation Modeling Without air resistance, projectile motion can be decomposed into horizontal uniform motion and vertical free-fall motion. Horizontal velocity remains constant while vertical velocity increases linearly under gravitational acceleration. The implementation requires solving differential equations: `x(t) = v0x*t` for horizontal motion and `y(t) = y0 + v0y*t - 0.5*g*t^2` for vertical motion, where `g` represents gravitational acceleration (typically 9.8 m/s²).

Inelastic Collision Handling When the object hits the ground, an inelastic collision occurs. Set a velocity decay coefficient of 40%, meaning the vertical velocity becomes 60% of its pre-collision value after impact. Horizontal velocity may also decay due to friction (parameters adjustable in code). This can be implemented using conditional statements checking `y_position <= 0` and applying velocity transformations: `vy_new = 0.6 * vy_old` and optional `vx_new = friction_coeff * vx_old`.

Simulation Loop and Visualization Use numerical iteration methods in MATLAB (such as Euler's method or more precise ODE solvers like `ode45`) to calculate position and velocity at each time step. Combine with `plot` or `animatedline` functions to update trajectories in real-time, creating dynamic visualization. The simulation loop typically involves time discretization with a `for` or `while` loop, position/velocity updates using kinematic equations, and real-time plotting commands within each iteration.

By adjusting initial parameters (initial velocity, launch angle, decay coefficients), users can observe different motion trajectories and collision effects, verifying physical principles through interactive simulation experiments.