Your inertia comment kept me (over)thinking for a while.
So what is inertia, and what makes it interesting on its own?
I guess we could describe it as v(t) = v(t - d) if a(t - d) = 0 for small d (velocity remains constant unless a force, i.e. acceleration, is applied) but this seems to be a bit self referential since it's just a longer way to say a(t) is v'(t).
What makes inertia interesting compared to other derivatives? Isn't acceleration "inertial" wrt jerk by definition? Or rather, any derivable function is "inertial" wrt to its derivative. Even if we had velocity change without external forces we'd just introduce a "phantom force" like gravity to make it all work nicely.
Is inertia as a concept just an artifact of classical physics being framed in terms of position and forces?
So what is inertia, and what makes it interesting on its own?
I guess we could describe it as v(t) = v(t - d) if a(t - d) = 0 for small d (velocity remains constant unless a force, i.e. acceleration, is applied) but this seems to be a bit self referential since it's just a longer way to say a(t) is v'(t).
What makes inertia interesting compared to other derivatives? Isn't acceleration "inertial" wrt jerk by definition? Or rather, any derivable function is "inertial" wrt to its derivative. Even if we had velocity change without external forces we'd just introduce a "phantom force" like gravity to make it all work nicely.
Is inertia as a concept just an artifact of classical physics being framed in terms of position and forces?