Zinovyeva Y. Exact solutions for the problem on the motion of two Lagrange gyroscopes connected by a spherical hinge

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0413U004698

Thesis Registration Form

0413U004698.pdf

Applicant for

Specialization

  • 01.02.01 - Теоретична механіка

02-07-2013

Specialized Academic Board

Д 11.193.01

Essay

The fourth form of equations of the inertial motion of two Lagrange gyroscopes, has been transformed into a nonhomogeneous second order differential equation with variable coefficients. The above equation is integrated by using five invariant relations of a special structure. Five new exact solutions of the problem. A new form of equations of the inertial motion of two Lagrange gyroscopes in the form of second kind Abel equations of has been deduced, for which integral cases have been obtained and six new exact solutions have been found. For each body, equations of hodographs in the supporting basis have been deduced. Such basis is introduced by using the trajectory of the hinge.

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