Equations of motion unsolvable with elementary method

[Robin04]

Hi,

Can you help me in collecting equations of motion that are unsolvable with elementary methods (especially with high school maths)? One that I found is when I release a body attached to an ideal spring that can freely rotate around an axis. The reason why I need them is because I would like to make simulations that can calculate a close outcome of the equation of motion.

Thanks for your answer in advance!

Robin

 

[FactChecker]

Are you looking for simple equations to check your simulation or are you looking for equations to use in your simulation? Real-world problems are usually too complicated to calculate a closed form solution. They are simulated in small time steps (say, 1/50 second). The forces and moments are calculated for the positions at one time. Then the motion is calculated for the small time step and new positions are obtained. Step through the simulation one time step (aka "time frame") at a time.

 

[Robin04]

After thinking it over again maybe that's not equations that I'm looking for. It would be much more fun to find my own equations. This example I wrote about was an exercise at a physics competition where only the situation/problem was described, and there was no information on how to solve this problem, they didn't even tell anything about the solvability. The method you described is the one that I used in my program. I determined what forces are acting on the body that are dependent on the position, expressed the acceleration, calculated the velocites and updated the positions.

 

[phyzguy]

A good example is the equation of motion for a simple pendulum. It is easily solvable if you make the small angle approximation, but for larger angles the solution requires elliptic functions. You could simulate a pendulum with a large angular displacement and show how the actual motion deviates from the sinusoidal motion predicted in the small angle limit.

 

[Robin04]

A good example is the equation of motion for a simple pendulum. It is easily solvable if you make the small angle approximation, but for larger angles the solution requires elliptic functions. You could simulate a pendulum with a large angular displacement and show how the actual motion deviates from the sinusoidal motion predicted in the small angle limit.

Thank you ver much. I'll try this one. :)

 

[Robin04]

I'm having some trouble with my first simulation :(
https://www.physicsforums.com/threads/whats-wrong-with-my-program.827883/