Introductory Rotational Dynamics

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Angular Momentum ◽  
Angular Displacement ◽  
Rigid Bodies ◽  
Rotational Dynamics ◽  
Circular Motion ◽  
Uniform Rotation ◽  
Chemical Systems ◽  
Inertial Frames ◽  
Rotating Frames ◽  
Special Case

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.

scholarly journals Rotation of inertial frames by angular momentum of matter and waves

2017 ◽  
Vol 34 (20) ◽  
pp. 205006
Author(s):  
W Barker ◽  
T Ledvinka ◽  
D Lynden-Bell ◽  
J Bičák
Keyword(s):  
Angular Momentum ◽  
Inertial Frames

Is angular impulse always equal to the change of angular momentum in collisions between rigid bodies?

1997 ◽  
Vol 18 (5) ◽  
pp. 363-368 ◽  
Author(s):  
M A Illarramendi ◽  
T del Río Gaztelurrutia ◽  
L M Villar
Keyword(s):  
Angular Momentum ◽  
Rigid Bodies ◽  
Angular Impulse

scholarly journals Coupled rotational dynamics of Jupiter's thermosphere and magnetosphere

2009 ◽  
Vol 27 (1) ◽  
pp. 199-230 ◽  
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.

scholarly journals Quantum angular momentum diffusion of rigid bodies

2017 ◽  
Vol 19 (12) ◽  
pp. 122001 ◽  
Author(s):  
Birthe Papendell ◽  
Benjamin A Stickler ◽  
Klaus Hornberger
Keyword(s):  
Angular Momentum ◽  
Rigid Bodies

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

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.

Die Pauli-Gleichung mit Differentialoperatoren für den Spin/ The Pauli Equation with Differential Operators for the Spin

1978 ◽  
Vol 33 (10) ◽  
pp. 1133-1150
Author(s):  
Eberhard Kern
Keyword(s):  
Angular Momentum ◽  
Rigid Body ◽  
Differential Operators ◽  
Spin Operator ◽  
Rigid Bodies ◽  
The Body ◽  
Wave Functions ◽  
Pauli Equation ◽  
Spin Eigenfunctions ◽  
Cartesian Coordinate

The spin operator s = (ħ/2) σ in the Pauli equation fulfills the commutation relation of the angular momentum and leads to half-integer eigenvalues of the eigenfunctions for s. If one tries to express s by canonically conjugated operators Φ and π = (ħ/i) ∂/∂Φ the formal angular momentum term s = Φ X π fails because it leads only to whole-integer eigenvalues. However, the modification of this term in the form s = 1/2 {π + Φ(Φ π) + Φ X π} leads to the required result.The eigenfunction system belonging to this differential operator s(Φ π) consists of (2s + 1) spin eigenfunctions ξm (Φ) which are given explicitly. They form a basis for the wave functions of a particle of spin s. Applying this formalism to particles with s = 1/2, agreement is reached with Pauli’s spin theory.The function s(Φ π) follows from the theory of rotating rigid bodies. The continuous spinvariable Φ = ((Φx , Φy, Φz) can be interpreted classically as a “turning vector” which defines the orientation in space of a rigid body. Φ is the positioning coordinate of the rigid body or the spin coordinate of the particle in analogy to the cartesian coordinate x. The spin s is a vector fixed to the body.

Rigid Body Collisions

1989 ◽  
Vol 56 (1) ◽  
pp. 133-138 ◽  
Author(s):  
Raymond M. Brach
Keyword(s):  
Energy Loss ◽  
Classical Problem ◽  
Negative Energy ◽  
Coefficient Of Restitution ◽  
Rigid Bodies ◽  
Interaction Process ◽  
Energy Losses ◽  
Conservation Of Energy ◽  
Special Case ◽  
Two Bodies

A general approach is presented for solving the problem of the collision of two rigid bodies at a point. The approach overcomes the difficulties encountered by others on the treatment of contact velocity reversals and negative energy losses. A classical problem is solved; the initial velocities are presumed known and the final velocities unknown. The interaction process between the two bodies is modeled using two coefficients. These are the classical coefficient of restitution, e, and the ratio, μ, of tangential to normal impulses. The latter quantity can be a coefficient of friction as a special case. The paper reveals that these coefficients have a much broader intepretation than previously recognized in the solution of collision problems. The appropriate choice of values for μ is related to the energy loss of the collision. It is shown that μ is bounded by values which correspond to no sliding at separation and conservation of energy. Another bound on μ combined with limits on the coefficient e, provides an overall bound on the energy loss of a collision. Examples from existing mechanics literature are solved to illustrate the significance of the coefficients and their relationship to the energy loss of collisions.

scholarly journals PROBES OF THE VACUUM STRUCTURE OF QUANTUM FIELDS IN CLASSICAL BACKGROUNDS

2002 ◽  
Vol 11 (01) ◽  
pp. 1-34 ◽  
Author(s):  
L. SRIRAMKUMAR ◽  
T. PADMANABHAN
Keyword(s):  
Lagrangian Approach ◽  
Quantum Fields ◽  
Flat Spacetime ◽  
Vacuum Structure ◽  
Effective Lagrangian ◽  
Inertial Frames ◽  
Different Types ◽  
Rotating Frames

We compare the different approaches presently available in literature to probe the vacuum structure of quantum fields in classical electromagnetic and gravitational backgrounds. We compare the results from the Bogolubov transformations and the effective Lagrangian approach with the response of monopole detectors (of the Unruh–DeWitt type) in noninertial frames in flat spacetime and in inertial frames in different types of classical electromagnetic backgrounds. We also carry out such a comparison in inertial and rotating frames when boundaries are present in flat spacetime. We find that the results from these different approaches do not, in general, agree with each other. We attempt to identify the origin of these differences and then go on to discuss its implications for classical gravitational backgrounds.

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