scholarly journals An approach in studying gyrostat motion with variable gyrostatic moment

2021 ◽  
Vol 31 (1) ◽  
pp. 102-115
Author(s):  
G.V. Gorr
Keyword(s):  
Fixed Point ◽  
Explicit Form ◽  
Poisson Equation ◽  
Mass Distribution ◽  
Equations Of Motion ◽  
Order System ◽  
Constant Multiplier ◽  
The Poisson Equation ◽  
Spherical Mass ◽  
Fifth Order

The problem of the motion of a gyrostat with a fixed point and a variable gyrostatic moment under the action of gravity force is considered. A new method for integrating the equations of motion of a system consisting of a carrier body and three rotors that rotate around the main axes is proposed. The method can be attributed to the method of variation of the constant in the function for the gyrostatic moment, which linearly depends on the vector of vertical. In case of a constant multiplier, the gyrostatic moment satisfies the Poisson equation, and its variation is found from the integral of areas. The original equations have been reduced to a fifth-order system. New solutions of these equations are obtained in the case of a spherical mass distribution for the gyrostat and for the precessional motions of a carrier body. An explicit form of the gyrostatic moment is established for the case of three invariant relations.

scholarly journals Mass Distribution and Gravitational Potential of the Milky Way

2017 ◽  
Vol 26 (1) ◽  
pp. 1-6
Author(s):  
Slobodan Ninković
Keyword(s):  
Exact Solution ◽  
Poisson Equation ◽  
Mass Distribution ◽  
Milky Way ◽  
Dark Halo ◽  
New Formalism ◽  
The Poisson Equation ◽  
Cumulative Mass ◽  
First Time ◽  
Special Case

AbstractModels of mass distribution in the Milky Way are discussed where those yielding the potential analytically are preferred. It is noted that there are three main contributors to the Milky Way potential: bulge, disc and dark halo. In the case of the disc the Miyamoto-Nagai formula, as simple enough, has shown as a very good solution, but it has not been able to satisfy all requirements. Therefore, improvements, such as adding new terms or combining several Miyamoto-Nagai terms, have been attempted. Unlike the disc, in studying the bulge and dark halo the flattening is usually neglected, which offers the possibility of obtaining an exact solution of the Poisson equation. It is emphasized that the Hernquist formula, used very often for the bulge potential, is a special case of another formula and the properties of that formula are analysed. In the case of the dark halo, the slopes of its cumulative mass for the inner and outer parts are explained through a new formalism presented here for the first time.

Sign in / Sign up

Export Citation Format

Share Document