Physics of Non-Inertial Reference Frames

TL;DR

This paper generalizes Newton's laws to non-inertial reference frames, introducing higher derivatives of motion as invariants and extending the dynamic law to account for forces affecting these derivatives.

Contribution

It proposes a new framework for physics in non-inertial frames using higher derivatives, extending classical laws to more general reference frames.

Findings

Kinematic invariants are higher derivatives of position.

Dynamic law relates forces to changes in higher derivatives.

Static law remains the sum of forces at rest.

Abstract

Physics of non-inertial reference frames is a generalizing of Newton's laws to any reference frames. The first, Law of Kinematic in non-inertial reference frames reads: the kinematic state of a body free of forces conserves and determinates a constant n-th order derivative with respect to time being equal in absolute value to an invariant of the observer's reference frame. The second, Law of Dynamic extended Newton's second law to non-inertial reference frames and also contains additional variables there are higher derivatives of coordinates. Dynamics Law in non-inertial reference frames reads: a force induces a change in the kinematic state of the body and is proportional to the rate of its change. It is mean that if the kinematic invariant of the reference frame is n-th derivative with respect the time, then the dynamics of a body being affected by the force F is described by the (n+1)-th differential equation. The third, Law of Static in non-inertial reference frames reads: the sum of all forces acting a body at rest is equal to zero.