On the trajectories of bodies in non-inertial reference frames. Part II

This paper provides a detailed solution to the problem of determining the trajectories of body motion in non-inertial frames of reference. The problem is solved in the basis τ, n, b moving along a given spatial curve. The orts of the basis are the vectors of the tangent τ, principal normal n, and binormal b to the curve. The motion of the noninertial frame of reference completely determines the vector of translational motion along the curve R0(t) with velocity v(t) = Ṙ0(t) τ and the Darboux vector of angular rotation ω = χτ + Kb . The curvature K and torsion χ are specified by the curve equation. Vectors τ, n, b are bound by the Frenet-Serret formulas. A system of second-order linear differential equations describing the free fall of a body from the point of view of an observer located in the basis T, n, b for cylindrical, hyperbolic, and conical helical lines is numerically analyzed. The corresponding trajectories of the bodies are plotted by computer modeling methods. A significant difference is observed in the trajectories of motion of one and the same body in the inertial and non-inertial frames of reference.

Keywords

Authors

References