On the first integrals of the problem of jumping a massive rigid body on a smooth horizontal plane

2004 ◽  
Vol 49 (6) ◽  
pp. 366-368
Author(s):  
A. A. Burov ◽  
D. P. Chevallier
1988 ◽  
Vol 26 (9) ◽  
pp. 575-576
Author(s):  
Duan Jihui ◽  
Charles T. P. Wang
Keyword(s):  

Author(s):  
Rodolfo Espindola-Heredia ◽  
Gabriela Del Valle ◽  
Damián Muciño-Cruz ◽  
Guadalupe Hernandez-Morales

In the children's movie The Incredibles there is a scene where Mr Incredible faces Bomb Voyage, while Incredi Boy wants to help Mr Incredible, Incredi Boy flies with Mr Incredible, who holds on to the hero's cloak, affecting Incredi Boy’s flight plan. To understand how an oscillatory movement affects non-oscillatory movement, an experimental prototype was constructed with a particle of mass m, attached to a rigid rod and without mass of length l, to a swivel of negligible mass, which was subject to a mass M. The swivel always remained on a horizontal plane, allowing the oscillatory movement of mass m. Experimental results were obtained by means of wireless sensors which recorded the spatial coordinates of the mass m. Using Lagrangian mechanics we obtained the equations of motion and expressed the possible first integrals of movement, when the movement of the mass M was: linear uniform (ULM), uniformly accelerated, (UAM), uniform circular (UCM), accelerated circular (ACM) and forced circular (FCM). The dynamics were analyzed, the equations of movement obtained, they were solved numerically, and the experimental results were compared to theoretical and numerical results.


2017 ◽  
Vol 44 (2) ◽  
pp. 169-180
Author(s):  
Alexander Karapetyan ◽  
Alexander Kuleshov

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.


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