Terminal parametrization for the final rotation vector of a solid body revolving around a fixed point

1988 ◽  
Vol 24 (11) ◽  
pp. 1132-1139
Author(s):  
Yu. A. Karpachev ◽  
Yu. M. Kuz'menko
Keyword(s):  
Fixed Point ◽  
Solid Body ◽  
Rotation Vector ◽  
Final Rotation

Kinematics and mass geometry for a solid body with a fixed point in ℝn

2001 ◽  
Vol 46 (9) ◽  
pp. 663-666
Author(s):  
D. V. Georgievskii ◽  
M. V. Shamolin
Keyword(s):  
Fixed Point ◽  
Solid Body

On the equations of rotation of a solid body about a fixed point

1864 ◽  
Vol 13 ◽  
pp. 52-64
Keyword(s):  
Fixed Point ◽  
Solid Body ◽  
The Body ◽  
Principal Axes ◽  
Usual Notation

In treating the equations of rotation of a solid body about a fixed point, it is usual to employ the principal axes of the body as the moving system of coordinates. Cases, however, occur in which it is advisable to employ other systems; and the object of the present paper is to develope the fundamental formulæ of transformation and integration for any system. Adopting the usual notation in all respects, excepting a change of sign in the quantities F, G, H, which will facilitate transformations hereafter to be made, let A = Σ m ( y 2 + z 2 ), B = Σ m ( z 2 + x 2 ), C= Σ m ( x 2 + y 2 ), -F = Σ myz , -G = Σ mzx , -H = Σ mxy ;

scholarly journals Global fixed points for nilpotent actions on the torus

2019 ◽  
Vol 40 (12) ◽  
pp. 3339-3367
Author(s):  
S. FIRMO ◽  
J. RIBÓN
Keyword(s):  
Fixed Point ◽  
Probability Measure ◽  
Nilpotent Group ◽  
Fixed Points ◽  
Nilpotent Groups ◽  
Rotation Vector

An isotopic to the identity map of the 2-torus, that has zero rotation vector with respect to an invariant ergodic probability measure, has a fixed point by a theorem of Franks. We give a version of this result for nilpotent subgroups of isotopic to the identity diffeomorphisms of the 2-torus. In such a context we guarantee the existence of global fixed points for nilpotent groups of irrotational diffeomorphisms. In particular, we show that the derived group of a nilpotent group of isotopic to the identity diffeomorphisms of the 2-torus has a global fixed point.

scholarly journals II. On the equations of rotation of a solid body about a fixed point

1863 ◽  
Vol 12 ◽  
pp. 523-524
Keyword(s):  
Fixed Point ◽  
Solid Body ◽  
The Body ◽  
Principal Axes

In treating the equations of rotation of a solid body about a fixed point, it is usual to employ the principal axes of the body as the moving system of coordinates. Cases, however, occur in which it is advisable to employ other systems; and the object of the present paper is to develope the fundamental formulæ of transformation and integration for any system.

Sign in / Sign up

Export Citation Format

Share Document