Most general dependence of acceleration

[fog37]

Hello,

Newton's second law, when the mass is constant, tells us that the acceleration $a=\frac {F}{m}$ which produces a simple ODE.

The acceleration is a function that can be constant $a= constant$, time-dependent $a(t)$, velocity-dependent $a(v)$, position dependent $a(x)$, etc.

What is the most general form of acceleration? Would it be $$a=a(x,t,v)$$ ?

Or can it depend on other variables, like higher order derivatives? I don't think so since those higher derivatives...

 

[FactChecker]

You should consider the state-space of the system you are considering. A state-space consists of all the information needed to specify the current state of the system. All the variables in the state-space may be needed to define the acceleration as a function.

That being said, if you know the time history of the velocity, then you can determine the acceleration from that as its derivative. Likewise, if you know the mass and force at any time, then the acceleration is $A = m/F$.