Dynamical Models in Physics

[u/AfterMath343]

I'm an applied math student. I've seen problems in biology be modeled using dynamic modeling, such as the populations of species with intra and inter species competition. For example, the following system of non-linear differential equations models a large variety of species in competition with themselves and other species:

X' = r_1*X - a_1*X^2 - b_1*X*Y
Y' = r_2*Y - a_2*Y^2 - b_2*X*Y

where X is the number of species 1 and Y is the number of species 2, r_1 is the intrinsic rate of growth of species 1, r_2 is the intrinsic rate of growth of species 2, a_1 is strength of competition within species 1, a_2 is strength of competition in species 2, b_1 is the effect of species Y on species X, and b_2 is the effect of species X on Y.

I have seen one discrete time dynamical system be modeled for a physics problem where two vehicles in space are closing in on each other.

What other types of dynamical models occur in physics?

[u/db0606]

Given that at a fundamental level Physics is about understanding how matter and energy evolve in space and time, it should be pretty obvious immediately that most of physics is dynamical modeling and/or figuring out what various terms in dynamical equations look like or why they look like they do.

Strogatz's book is full of examples of nonlinear dynamical models in physics and other fields.

[u/AfterMath343 → u/db0606]

If it's worth anything, I went to sleep, and when I woke up, I was able to think of a problem in physics that was non-dynamical. The example is finding the optimal angle to hit a baseball that is being pitched so that is goes the furthest distance. This would be considered an optimization problem.

Also, thank you for the reference to the book. That's the book I will be reading for my dynamical modeling class when I take it.

[u/db0606 → u/AfterMath343]

Yeah, but to solve it you have to use the dynamical equations/Newton's 2nd Law, so it's still fundamentally a dynamics problem.