Issue 1, 2016
Study of the unit “Rotational motion of a rigid body” in the course of general physics
Study of the unit “Rotational motion of a rigid body” in the course of general physics
D.V. Belov, A.S. Nifanov, I.M. Sraeva
This paper is a preamble to the detailed presentation of the classical mechanics unit “Rotational motion of a rigid body” for minor students in higher school. It clarifies the meaning of notions and definitions used in this unit, such as the rotational motion about an axis, moment of inertia, angular momentum, instantaneous axis of rotation, ellipsoid of inertia, and inertia tensor.
Show AbstractGeometric phase transition in the problem of brachistochrone
Geometric phase transition in the problem of brachistochrone
Gladkov S.O., Bogdanova S.B.
It is found analytical solution of problem I. Bernoulli on the brahistohrone with frictional forces (viscous, proportional to speed motion and dry). It is shown that its solution is represented only in the form quadratures. With the aid of the numerical calculation are given different figures of optimum trajectories under dissipation conditions. It is proven that in the absence frictional forces any motion along the curvilinear chute under the action only of gravitational force is always reduced to the task about the brahistohrone. It is found the point “geometric phase transition”. This point corresponds to the disruption of brahistohrones from one class of trajectories to qualitatively another class. It is shown that with steady state the trajectory takes the form of the usual parabola, motion along which is periodically like the pendulum.
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