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Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)
Quaternion Solution for the Rock’n’roller: Box Orbits, Loop Orbits and Recession
Peter Lynch, Miguel D. Bustamante School of Mathematical Sciences, UCD, Belfield, Dublin 4, Ireland
Аннотация:
We consider two types of trajectories found in a wide range of mechanical systems, viz. box orbits and loop orbits. We elucidate the dynamics of these orbits in the simple context of a perturbed harmonic oscillator in two dimensions. We then examine the small-amplitude motion of a rigid body, the rock’n’roller, a sphere with eccentric distribution of mass. The equations of motion are expressed in quaternionic form and a complete analytical solution is obtained. Both types of orbit, boxes and loops, are found, the particular form depending on the initial conditions. We interpret the motion in terms of epi-elliptic orbits. The phenomenon of recession, or reversal of precession, is associated with box orbits. The small-amplitude solutions for the symmetric case, or Routh sphere, are expressed explicitly in terms of epicycles; there is no recession in this case.
Ключевые слова:
rolling body dynamics, nonholonomic constraints, Hamiltonian dynamics.
Поступила в редакцию: 28.06.2012 Принята в печать: 05.12.2012
Образец цитирования:
Peter Lynch, Miguel D. Bustamante, “Quaternion Solution for the Rock’n’roller: Box Orbits, Loop Orbits and Recession”, Regul. Chaotic Dyn., 18:1-2 (2013), 166–183
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd103 https://www.mathnet.ru/rus/rcd/v18/i1/p166
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