Abstract:
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 $\tau$, $\mathbf{n}$, $\mathbf{b}$ moving along a given spatial curve. The orts of the basis are the vectors of the tangent $\tau$, principal normal $\mathbf{n}$, and binormal $\mathbf{b}$ to the curve. The motion of the noninertial frame of reference completely determines the vector of translational motion along the curve $\mathbf{R}_0(t)$ with velocity $\mathbf{v}(t) = \dot R_0(t) \tau$ and the Darboux vector of angular rotation $\omega = \chi\tau + K\mathbf{b}$. The curvature $K$ and torsion $\chi$ are specified by the curve equation. Vectors $\tau$, $\mathbf{n}$, $\mathbf{b}$ 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 $\tau$, $\mathbf{n}$, $\mathbf{b}$ 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.
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