scholarly journals The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere

2013 ◽  
pp. 141-202 ◽  
Author(s):  
A. V. Borisov ◽  
◽  
I. S. Mamaev ◽  
I. A. Bizyaev ◽  
◽  
...  
Keyword(s):  
Rigid Body ◽  
Body Rolling ◽  
Rolling Without Slipping

The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere

2013 ◽  
Vol 18 (3) ◽  
pp. 277-328 ◽  
Author(s):  
Alexey V. Borisov ◽  
Ivan S. Mamaev ◽  
Ivan A. Bizyaev
Keyword(s):  
Rigid Body ◽  
Body Rolling ◽  
Rolling Without Slipping

Experimental Determination of Steady and Unsteady Loads on a Surface Piercing, Ventilated Hydrofoil

1969 ◽  
Vol 13 (01) ◽  
pp. 1-11
Author(s):  
G. E. Ransleben
Keyword(s):  
Rigid Body ◽  
Experimental Determination ◽  
Cross Section ◽  
Angle Of Attack ◽  
Chord Length ◽  
Body Rolling

Measured steady and unsteady section lift and moment coefficients at two spanwise locations on a surface-piercing ventilated hydrofoil are presented. The foil, of wedge cross section, was supported vertically, and submerged one chord length from the tip. Excitation in rigid-body rolling and pitching modes to the cantilevered foil produced the unsteady loads. All tests were made at a nominal angle of attack of 12 deg.

Experimental Determination of Steady and Unsteady Loads on a Submerged Supercavitating Hydrofoil

1968 ◽  
Vol 12 (02) ◽  
pp. 89-104
Author(s):  
Guido E. Ransleben
Keyword(s):  
Steady State ◽  
Aspect Ratio ◽  
Rigid Body ◽  
Experimental Determination ◽  
Data Reduction ◽  
Noise Levels ◽  
Considerable Difficulty ◽  
High Noise ◽  
Body Rolling

Measured spanwise distributions of steady-state and oscillatory lift and moment on a fully submerged supercavitating hydrofoil are presented. The foil had a rectangular planform of aspect ratio 5, and was excited in rigid-body rolling and pitching modes for the oscillatory tests. Considerable difficulty was experienced in the data reduction because of high noise levels, but a significant amount of data was recovered. All tests were made at a single angle of attack of 1 2 deg.

On the Computation of Relative Rotations and Geometric Phases in the Motions of Rigid Bodies

1997 ◽  
Vol 64 (4) ◽  
pp. 969-974 ◽  
Author(s):  
O. M. O’Reilly
Keyword(s):  
Rigid Body ◽  
Computational Methods ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Relative Rotation ◽  
Geometric Phases ◽  
Body Dynamics ◽  
Computational Aspects ◽  
Body Rolling ◽  
The Moment

In this paper, expressions are established for certain relative rotations which arise in motions of rigid bodies. A comparison of these results with existing relations for geometric phases in the motions of rigid bodies provides alternative expressions of, and computational methods for, the relative rotation. The computational aspects are illustrated using several examples from rigid-body dynamics: namely, the moment-free motion of a rigid body, rolling disks, and sliding disks.

scholarly journals Note on a ball rolling over a sphere: Integrable Chaplygin system with an invariant measure without Chaplygin hamiltonization

2019 ◽  
Vol 46 (1) ◽  
pp. 97-108 ◽  
Author(s):  
Bozidar Jovanovic
Keyword(s):  
Invariant Measure ◽  
Rigid Body ◽  
Cotangent Bundle ◽  
Multiplier Method ◽  
Ball Rolling ◽  
Chaplygin System ◽  
Rolling Without Slipping ◽  
Body Inertia

In this note we consider the nonholonomic problem of rolling without slipping and twisting of an ??-dimensional balanced ball over a fixed sphere. This is a ????(??)?Chaplygin system with an invariant measure that reduces to the cotangent bundle ??*?????1. For the rigid body inertia operator r I? = I? + ?I, I = diag(I1,...,In) with a symmetry I1 = I2 = ... =Ir ? Ir+1 = Ir+2 = ... = In, we prove that the reduced system is integrable, general trajectories are quasi-periodic, while for ?? ? 1, ?? ? 1 the Chaplygin reducing multiplier method does not apply.

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