# Nonlinear impact model of a tennis racket and a ball

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Farnam on 27 Jan 2024
Commented: Benjamin Thompson on 28 Jan 2024
I want to model the impact of a tennis ball on the center of the string of a tennis racket in a non-linear way, so that the ball is modeled with a mass system and a linear spring and damper, and the racket string is modeled as a non-linear spring, and the racket frame Consider a solid body.

Benjamin Thompson on 27 Jan 2024
Try the MATLAB or Simulink OnRamp training, then attempt to create your model. If you run into problems then ask specific questions.
Farnam on 27 Jan 2024
Thank you for your response In solving the equations of this system, I rich to three equations that these non-linear equations must be solved as a couple, and I could not find the correct answer in solving these equations in MATLAB.(initial conditions can also be assumed arbitrary) 1)mby``+cb(yb'-yj`)+kb(yb-yj)=0 2)cb(yb`-yj`)+kb(yb_yj)=fsb 3)mre(yr``)-fsb=0 mb=ball mass cb=damping constant kb=spring constant fsb=nonlinear spring force=ay^3+by^2+cy
Benjamin Thompson on 28 Jan 2024
Can you write these equations in MATLAB code or in math notation? It is hard to understand the equations in your comment. They appear to be differential equations, so what solution are you looking for?
Here is MATLAB documentation on differential equation solving functions with several examples:

Sam Chak on 27 Jan 2024
I wanted to share that Andre Agassi is my all-time favorite professional tennis player. When observing the motion of a tennis ball, it becomes apparent that it does not conform to the behavior of a typical mass-spring-damper system. Unlike the predictable stability of a 2nd-order mass-spring-damper system, the tennis ball follows curved trajectories due to the combined influences of gravity and the Magnus force which is induced by the spin of the ball (you'll encounter this term in your studies of Aerodynamics).
John D'Errico on 28 Jan 2024
Of course, the Magnus effect only impacts the ball after it has left the racket. Since the apparent goal of the simulation stops after the ball leaves the racket, that would seem irrelevant.
I would suggest it is far more important to consider the ball as not a solid body, in terms of its interaction with the strings.