scholarly journals On Detachment Conditions in the Problem on the Motion of a Rigid Body on a Rough Plane

2008 ◽  
pp. 287-302
Author(s):  
A. P. Ivanov ◽  
Keyword(s):  
Rigid Body ◽  
Rough Plane

On dynamics of a rigid body on a moving rough plane

2017 ◽  
Vol 87 (5) ◽  
pp. 829-839 ◽  
Author(s):  
Yury Selyutskiy ◽  
Rinaldo Garziera ◽  
Luca Collini
Keyword(s):  
Rigid Body ◽  
Rough Plane

scholarly journals The Routh theorem for mechanical systems with unknown first integrals

2017 ◽  
Vol 44 (2) ◽  
pp. 169-180
Author(s):  
Alexander Karapetyan ◽  
Alexander Kuleshov
Keyword(s):  
Rigid Body ◽  
Mechanical Systems ◽  
First Integrals ◽  
Rotationally Symmetric ◽  
Rough Plane ◽  
Symmetric Rigid Body

In this paper we discuss problems of stability of stationary motions of conservative and dissipative mechanical systems with first integrals. General results are illustrated by the problem of motion of a rotationally symmetric rigid body on a perfectly rough plane.

scholarly journals I. Note on Professor Sylvester’s representation of the motion of a free rigid body by that of a material ellipsoid whose centre is fixed, and which rolls on a rough plane

1870 ◽  
Vol 160 ◽  
pp. 1-7 ◽  
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Royal Society ◽  
Moments Of Inertia ◽  
Fixed Plane ◽  
Free Rigid Body ◽  
Principal Moments Of Inertia ◽  
Rough Plane ◽  
Important Extension

In a paper published in the Transactions of the Royal Society for 1866, Professor Sylvester has given an important extension of Poinsot’s representation of the motion of a freely rotating rigid body, by means of the momental ellipsoid. He has proved that if a material ellipsoid, similar in form to the momental ellipsoid, and so constituted that its principal moments of inertia, A, B, C, are connected with its semiaxes a , b , c by the rela­tion A a 4 ( b 2 — c 2 ) + B b 4 ( c 2 — a 2 ) + Cc 4 ( a 2 — b 2 ) = 0, be made to roll in contact with a perfectly rough plane, the motion of this material ellipsoid will be precisely the same as that of the momental ellipsoid of the rigid body; the rough plane taking the place of the geo­metrical fixed plane, in contact with which the momental ellipsoid is supposed to roll. He has also investigated expressions for the pressure and friction between the ellipsoid and the rough plane, in terms of the angular velocity of the ellipsoid, and of the length of its axes, and the distance of the centre from the rough plane. In investigating inde­pendently the values of these forces, I have been led to a somewhat different treatment of the same problem, in the course of which some theorems have presented themselves which may be not without interest.

scholarly journals I. Note on Professor Sylvester’s representation of the motion of a free rigid body by that of a material ellipsoid rolling on a rough plane

1869 ◽  
Vol 17 ◽  
pp. 470-472
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Constant Component ◽  
Free Rigid Body ◽  
Angular Momenta ◽  
Rough Plane ◽  
Instantaneous Axis

This paper is intended as a sequel to Professor Sylvester’s paper above mentioned, which was published in the Philosophical Transactions for 1866. The notation, so far it differs from Professor Sylvester’s, is as follows:- p is the distance from the centre of the ellipsoid to the rough plane. λ the (constant) component angular velocity of the ellipsoid about the diameter normal to the rough plane, the component angular velocity of the ellipsoid about the diameter parallel to the projection of the instantaneous axis on the rough plane. h λ ., h p are the component angular momenta about these diameters respectively. h t about the diameter at right angles to both. n the angular velocity, in space, of the plane through the instantaneous axis perpendicular to the rough plane.

scholarly journals Dynamics of rigid body, carrying moving masses and rotor, on a rough plane

2012 ◽  
pp. 763-772 ◽  
Author(s):  
A. P. Ivanov ◽  
◽  
A. V. Sakharov ◽  
Keyword(s):  
Rigid Body ◽  
Dynamics Of Rigid Body ◽  
Rough Plane
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