Rotational dynamics of celestial bodies: Generalized rotation and considerations of angular momentum

This chapter discusses the importance of circular motion and rotations, whose applications to chemical systems are plentiful. Circular motion is the book’s first example of a special case of motion using the laws developed in previous chapters. The chapter begins with the basic definitions of circular motion; as uniform rotation around a principle axis is much easier to consider, it is the focus of this chapter and is used to develop some key ideas. The chapter discusses angular displacement, angular velocity, angular momentum, torque, rigid bodies, orbital and spin momenta, inertia tensors and non-inertial frames and explores fictitious forces as well as transformations in rotating frames.

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Rotational dynamics of celestial bodies

Astrophysics and Space Science ◽

10.1007/bf02463871 ◽

1985 ◽

Vol 114 (1) ◽

pp. 175-189

Author(s):

V. S. Geroyannis

Keyword(s):

Rotational Dynamics ◽

Celestial Bodies

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Coupled rotational dynamics of Jupiter's thermosphere and magnetosphere

Annales Geophysicae ◽

10.5194/angeo-27-199-2009 ◽

2009 ◽

Vol 27 (1) ◽

pp. 199-230 ◽

Cited By ~ 39

Author(s):

C. G. A. Smith ◽

A. D. Aylward

Keyword(s):

Angular Momentum ◽

Momentum Transfer ◽

Electric Fields ◽

Joule Heating ◽

Rotational Dynamics ◽

High Latitudes ◽

Inner Magnetosphere ◽

Angular Momentum Transfer ◽

Simple Physical Model ◽

Low Latitudes

Abstract. We describe an axisymmetric model of the coupled rotational dynamics of the thermosphere and magnetosphere of Jupiter that incorporates self-consistent physical descriptions of angular momentum transfer in both systems. The thermospheric component of the model is a numerical general circulation model. The middle magnetosphere is described by a simple physical model of angular momentum transfer that incorporates self-consistently the effects of variations in the ionospheric conductivity. The outer magnetosphere is described by a model that assumes the existence of a Dungey cycle type interaction with the solar wind, producing at the planet a largely stagnant plasma flow poleward of the main auroral oval. We neglect any decoupling between the plasma flows in the magnetosphere and ionosphere due to the formation of parallel electric fields in the magnetosphere. The model shows that the principle mechanism by which angular momentum is supplied to the polar thermosphere is meridional advection and that mean-field Joule heating and ion drag at high latitudes are not responsible for the high thermospheric temperatures at low latitudes on Jupiter. The rotational dynamics of the magnetosphere at radial distances beyond ~30 RJ in the equatorial plane are qualitatively unaffected by including the detailed dynamics of the thermosphere, but within this radial distance the rotation of the magnetosphere is very sensitive to the rotation velocity of the thermosphere and the value of the Pedersen conductivity. In particular, the thermosphere connected to the inner magnetosphere is found to super-corotate, such that true Pedersen conductivities smaller than previously predicted are required to enforce the observed rotation of the magnetosphere within ~30 RJ. We find that increasing the Joule heating at high latitudes by adding a component due to rapidly fluctuating electric fields is unable to explain the high equatorial temperatures. Adding a component of Joule heating due to fluctuations at low latitudes is able to explain the high equatorial temperatures, but the thermospheric wind systems generated by this heating cause super-corotation of the inner magnetosphere in contradiction to the observations. We conclude that the coupled model is a particularly useful tool for study of the thermosphere as it allows us to constrain the plausibility of predicted thermospheric structures using existing observations of the magnetosphere.

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Experiments on Motion Control of Two-Joint Articulated Hopping Robot with Stopper Mechanisms

Journal of Robotics and Mechatronics ◽

10.20965/jrm.2005.p0089 ◽

2005 ◽

Vol 17 (1) ◽

pp. 89-100

Author(s):

Gustavo Kato ◽

◽

Hiroyuki Kojima ◽

Mamoru Yoshida ◽

Yusuke Wakabayashi ◽

...

Keyword(s):

Angular Momentum ◽

Control System ◽

Motion Control ◽

Dc Motor ◽

Rotational Dynamics ◽

Control Voltage ◽

Dc Motors ◽

Hopping Robot ◽

New Type ◽

Motion Performance

In this report, a new-type two-joint articulated hopping robot with two stopper mechanisms is developed. The two rotary joints are actuated by two DC motors with reduction gears. In this new-type two-joint articulated hopping robot with two stopper mechanisms, the hopping motion actions are achieved by the two joint rotational dynamics and the two stopper mechanisms. Using the two stopper mechanisms, the angular momentums and momentums of the two links are transformed into the hopping motion action according to the law of conservation of angular momentum and momentum. Then, the hopping motion control system is constructed to fit the DC motor characteristics, and the effects of the stopper settings and the delay time of the control voltage of the DC motor on the hopping motion performance are experimentally investigated. Furthermore, the examples of the hopping motion control experiments are demonstrated, and it is confirmed that the forwards and backwards hopping motion actions can be successfully performed.

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