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TRAPPIST-1 harbors at least 7 Earth-mass planets orbiting a 0.089 solar mass dwarf M-star. Numerous other multi-planetary systems have been detected and all obey a quantization of angular momentum per unit mass constraint predicted by quantum celestial mechanics (QCM) as derived from the general theory of relativity (GTR). The universality of this constraint dictates that the TRAPPIST-1 system should obey also. I analyze this recently discovered system with its many mean motion resonances (MMRs) to determine its compliance and make some comparisons to the Solar System and 11 other multi-planetary systems., 1 Introduction In the past 25 years, more than 3500 exoplanets have been detected, many in multi-planetary systems with 4 or more planets [1]. Extreme examples include HD 10180 with [...]

In July, 2015, the New Horizons spacecraft passing by Pluto did not discover any more moons. Therefore, we know the Pluto system total angular momentum to within 2.4%, more accurately than any other system with more than two orbiting bodies. We therefore update our previous analysis to determine whether a definitive test of the quantum celestial mechanics (QCM) angular momentum constraint can now be achieved., 1 Introduction In 2012 we analyzed the angular momentum properties of the Pluto system with its 5 moons [1] not knowing the total angular momentum in the system. The New [...]

The angular momentum operator [??] of a particle obeys the usual commutation rule [??] X [??] = ih[??]. In contrast, the total angular momentum operator [??] of a set of particles relative to moving axes (as, for instance, when mounted on a tumbling molecule) obeys the anomalous commutation rule [??] X [??] = -ih[??]. We give a pedagogical and mathematically nonsophisticated description of intermediate cases for which partial angular momentum operators, relative to various moving frames, obey unusual commutation relations that are neither usual nor anomalous. Insight into the origin of these unusual commutation relations provides a means of guessing the type of commutation rule that will be obeyed. In particular, it gives a way to avoid, as far as possible, the unusual commutation relations, which lead to complicated and nonsystematic expressions. Some examples from molecular physics are presented. [c] 2010 American Association of Physics Teachers. [DOI: 10.1119/1.3482257]

The life cycle of the 2 June 1995 Dimmitt, Texas, tornado cyclone, observed during the Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX), is described. The tornado cyclone here is defined as a significantly axisymmetric flow larger than the visible tornado and characterized by increasing angular momentum with increasing radius. Its life cycle included three phases with somewhat differing evolution of angular momentum, herein called intensifying, transition, and weakening. During the intensifying stage, the funnel and debris cloud gradually increased in size. The azimuthally averaged secondary circulation of the larger-scale tornado cyclone, as determined using high-resolution single-Doppler data obtained by a mobile radar, was primarily inward and upward, consistent with the presence of a wall cloud outside the tornado. The azimuthally averaged angular momentum increased monotonically away from the tornado, so inward advection allowed the angular momentum to increase slowly with time in part of the tornado cyclone. During the transition phase, downdrafts began to occur within the tornado cyclone. The transport of angular momentum by the secondary circulation nearly was offset by eddy flux convergence of angular momentum so that the azimuthally averaged angular momentum tendency was only weakly negative at most radii. The tornado was visually impressive during this stage, featuring a 400-m diameter debris cloud extending to cloud base, while the surrounding wall cloud shrank and eroded. During the weakening phase, the funnel and debris cloud gradually shrank, and the funnel went through a rope stage prior to disappearing. The weakening phase was characterized by extensive downdrafts at all radii outside the tornado, and large-scale near-ground outflow as observed by mobile mesonet systems in a portion of the tornado cyclone. The secondary circulation acted to transport smaller angular momentum downward from aloft, and outward along the ground. All terms of the angular momentum budget became negative throughout most of the low-level (0-800-m AGL) tornado cyclone during the weakening phase. Several hypotheses for this evolution are evaluated, including changes in water loading in the tornado cyclone, cooling of the near-ground air, and the distribution of tangential velocity with height with its concomitant influence on the nonhydrostatic vertical pressure gradient force.

Strontium ruthenate's superconductivity takes place in the parallel planes formed by its ruthenium and oxygen atoms. When the electrons pair up below the critical temperature, their spin angular momenta (blue arrows) rotate in the plane, with their orbital angular momenta pointing out of the plane, and if one could reverse the pairs' spin and motion, their total orbital angular momentum would flip breaking time-reversal symmetry.

A time-dependent wave packet study is reported in which the feasibility of initiating the hydrogen exchange reaction is investigated in the Cl((super 2)P) + HCl by vibrational excitation of the HCl molecule. The effect of substitution of either of the Cl atoms by (super 37)Cl on the reaction is very small, the product state distributions are affected very slightly and a change in rotational and electronic product state distributions is observed for the products after reaction as compared to direct dissociation.

The complex-forming CH+H2 --> CH2+H reaction is studied employing a global potential energy function, and the reaction probability in the total angular momentum J=0 limit is estimated with a four-atom quantum wave packet method. The results show that there are angular constraints to complex formation and the zero-energy violation in the trajectories is a particularly severe problem for the reaction.

The angular momentum of a steady, axially symmetric distribution of electromagnetic fields is shown to be expressible as [L.sub.em]=[integral]dQrXA, where dQ is an element of moving charge at position r and A is the local vector potential. This result, which is valid for relativistic motion, gives an easy way of calculating the angular momentum of symmetric distributions of charges or currents. A consequence of this result is that in the nonrelativistic limit, the magnetic energy of the distribution can be expressed solely in terms of the angular momentum [L.sub.em] and the angular velocity of the rotating system, k[omega], as [U.sub.mag]=l/2(k[omega]) * [L.sub.em]. This result is applied to three uniform, nonrelativistic, spinning charge distributions: a cylindrical shell, a spherical shell, and a solid sphere. [DOI: 10.1119/1.2165246]

Nearside-farside and local angular momentum techniques, originally developed for the analysis of collision at fixed total energies are applied to the plane wave packet (PWP) theory of time-dependent scattering and the H + D2 reaction is studied. This becomes possible due to the PWP theory employs concepts and formulas analogues to those found in time-independent scattering theory.

Many asset pricing anomalies can be explained by mental accounting and prospect theory frameworks. The intention behind momentum existing in the cross section of stock returns is explained by this paper model of equilibrium asset prices.

The magnetization dynamic in ferromagnetic heterostructures from first principles, focusing on the role of spin pumping in layered structures is reviewed. It is based on the assumption of semiclassical transport in bulk materials that is valid for diffuse and chaotic systems, as well as a separation of time scales of the electronic and magnetic degrees of freedom.

The dynamical behavior of a simple rotating mechanical system that carries a charge on its surface and is accelerated by a falling mass is considered. It is shown that a fraction of the total kinetic energy is missing and that exactly this fraction of energy has been stored in the magnetic field distribution. The conservation of electromagnetic angular momentum is also discussed on the same basis. The concept of an electromagnetic moment of inertia is introduced to establish a close parallel with the concept of mechanical moment of inertia in classical dynamics. It is suggested that the present mechanical system can be used as a teaching tool at the early-to-intermediate level of an undergraduate physics program to ease the transition from the dynamics of rigid bodies to that of more abstract fields. [DOI: 10.1119/1.1485715]

Molecular dynamics simulations of acetylcholine, in terms of solvent-influenced solute molecules motion, reveal seven clusters of conformers. Data indicate a progressive loss of conformational freedom and a decrease in angular velocity and angular acceleration with increasing molecular weight of the solvents.

This paper is concerned with the integration of the differential equations for the Euler parameters, for the purpose of describing the orientation of a rigid body. This can be done using standard methods, but in some cases, such as in the presence of impulsive forces, the angular velocities are not continuous and methods based on high order continuity are not appropriate. In this paper, the use of the closed-form solution for piecewise constant angular velocity as the basis for a computational algorithm is studied. It is seen that if this solution is implemented in a leapfrog manner a method with second-order accuracy is obtained in the smooth case, while this method also makes sense in the discontinuous case.

Research has been conducted on the photodissociation reaction event occurring under the energy constraint and angular momentum angulation. The analysis of this reaction which is a molecular reaction driven by light energy is presented.

A study of the three-dimensional wave packet calculations for total momentum quantum number J greater or equal to zero is performed using Jacobi coordinates is presented. The results show that a wave packet representing a rotating triatomic molecule is propagated in Jacobi coordinates for total angular momentum quantum number J equal to 0, 1, and 2.

A theoretical study of the highest bound states and lowest energy resonance states of water in its ground electronic state, with zero total angular momentum, is discussed. Resonance with hyperspherical and local mode character is observed.

A computational method for the calculation of quantum state-to-state reactive probabilities for the reduced dimensionality is presented. The three degree of freedom, AB+CDA+BCD reactions is presented.

Byline: A.Ya. Tsaune (1) Keywords: complete and rovibronic Hamiltonians; laboratory and molecular infinitesimal variables; dynamic and deformation rotations of the principal axes; fundamental tensors; coefficients of connectedness; object of anholonomity; Jacobians of transformations Abstract: This paper is concerned with derivation of a complete Hamiltonian and its rovibronic part containing no anomalous (singular) coefficients like I .sub.[alpha]/2(I .sub.[beta]-I .sub.I3).sup.2 by the square components of the orbital angular momentum for an N-particle system. The work consists of two parts. In the first part the reasons for appearance of the anomalies (in earlier papers as well as in more recent ones ) are analyzed and a general procedure of removing the singularities is proposed through the correct consideration of both determination of the angular momentum and mutual displacements of the particles. The complete description of transition from laboratory variables to molecular ones including non-holonomic coordinates is presented. In the second part the explicit expressions of the Hamiltonians are obtained through the use of tensor methods. The first of them is as follows: H = 1/2M[summation with index].sub.[alpha] P.sub.[alpha] P.sub.[alpha] + [summation with index].sub.[alpha] 1/2I.sub.[alpha] L.sub.[alpha] L.sub.[alpha] + 1/2[summation with index].sub.j [summation with index].sub.k g.sup.jk [summation with index].sub.[alpha] 1/I.sub.[alpha] W.sub.1.sup.[alpha] L[alpha] Here P .sub.[alpha], L .sub.[alpha], p .sub.k are the components of the total momentum, the angular momentum and momenta of internal motion. Author Affiliation: (1) Ukrainian State Chemical and Technological University, av. Yu. Gagarin 8, 49005, Dnepropetrovsk, Ukraine Article History: Registration Date: 11/01/2005

The product energy and angular momentum distribution for dissociation of the Al(sub 6) and Al(sub 13) clusters are presented which are compared with the predictions of statistical theories. The report stated that EngelRing model for deducing the cluster dissociation energy from the measured does not give accurate results for Al(sub 6) and Al(sub 3) dissociations.

We describe a new undergraduate mechanics laboratory experiment that illustrates principles of linear and angular momentum conservation. Students observe that angular momentum is conserved in systems where the initial conditions involve only translational motion, and yet the final conditions include rotational motion. To do this, students make a digital video of a two-object collision on an air table. One object has an asymmetric mass distribution and gains rotational kinetic energy as a result of the collision. Using their digital video, students create a stroboscopic image of the two objects' trajectories and show that both linear and angular momentum are conserved to within a few percent, the limit of experimental uncertainty. Students also show that angular momentum conservation is independent of the choice of origin, that the center of mass of the asymmetric object follows a linear trajectory, and that the center of mass of the whole system follows a linear trajectory. c 2000 American Association of Physics Teachers.

A rotating block method is developed to calculate the rotational displacements of gravity retaining walls based on rigid foundations under seismic loading. The method is similar to the pseudostatic sliding block method of Newmark. When a threshold acceleration for rotation is exceeded, a rigid wall will start to rotate until the angular velocity for rotation is reduced to zero. The influence of ground motion characteristics on computed wall deformation was evaluated. The procedure was validated by data from centrifuge tests. This method is also applicable for the most complex cases when the sliding and rotation of a gravity wall are coupled.

A rod, connected with a horizontal hinge to the vertical axle of a motor, will deviate from the vertical at angular frequencies of the motor above a certain minimum value. The acceleration of gravity is related in a simple way to the speed of the motor, the length of the rod, and its angle with the vertical. It turns out that g can be measured in this way with an accuracy of about 0.1% without the use of sophisticated technology or the application of corrections to the result. The system has some other interesting features which make it particularly appropriate for the undergraduate laboratory.

Results demonstrate that angular distribution of ejected particles follows Gaussian curve with smooth surface particles at the center and those of the rough surface randomly scattered. Data further indicate that increasing laser fluence increases the energy of the ejected particles

Abstract: Cross-term conservation relationships for electromagnetic energy, linear momentum, and angular momentum are derived and discussed here. When two or more sources of electromagnetic fields are present, these relationships connect the cross terms that appear in the traditional expressions for the electromagnetic (1) energy, (2) linear momentum, and (3) angular momentum, over to, respectively, (1) the sum of the rates of work, (2) the sum of the forces, and (3) the sum of the torques, that are due to the fields of each charge or current source acting upon the other charge and current sources. These relationships, although not new, appear to be rarely recognized and used in the physics literature. As shown here, they can be extremely helpful for solving and gaining a deeper physical understanding into a rather diverse range of interesting problems in electrodynamics, including (1) aspects of Poynting's theorem when applied to charged point particles, (2) the detailed physical basis of electrostatic analysis, (3) understanding the connection between different techniques used in the past for solving Casimir force problems, and (4) reconciling the invalidity of Newton's third law in electrodynamics. Article History: Registration Date: 08/10/2004

Net momentum and torque during a cat twist is zero, as revealed by a study of the motion of twisting by a mechanical cat model. A simplified mechanical cat consisting of an elastic cord attached to two similar parts joined by a central spring reveals that the torque-free twist performed by the mechanical cat model presents a simpler and identical performance of the real cat twist. The possibility of similar torque-free twists by other animals is discussed.

Small deformations are included in the expression, in floating coordinates, of the angular momentum of a torque-free deforming axisymmetric gyro in relation to inertia moments and angular velocity components. The general form of the angular momentum expression is initially obtained. Angular momentum components for arbitrarily large deformations are estimated from the expression of angular momentum in matrix form.

Analyses of a near-symmetric rigid body undergoing time-varying torques which are expressed as polynomial functions involved a derivation of analytic solutions. The torque around the spinning axis is hypothesized to stay unchanged. Derivations were obtained in the case of the angular velocity vector and the Eulerian angles. The solution of the angular velocities are precise in cases where the rigid body is axisymmetric.

Differential rotation and localized Keplerian shear in the nebula cause turbulence in solar nebula. Infinitesimal perturbations of the Keplerian shear has no relation to the turbulence. Pressure fluctuations, planetesimal interactions and material infall cause the Keplerian shear.

Fluctuations in the global angular momentum of a two-layer zonally homogeneous global model of the atmosphere are dominated by very low frequencies, periods longer than 100 days. This variability is confined to the tropics, where it is associated with variations of approximately [+ or -] 5 m [s.sup.-1] in the zonal winds. Lagged correlations suggest that the variations in angular momentum are a response to variability in the zonally averaged eddy flux of vorticity in the tropics. A zonally symmetric model is constructed to determine the response to an impulsive rearrangement of vorticity across the tropics. The response of the angular momentum in the zonally symmetric model in convolution with the tropical eddy flux of vorticity derived from the full model, provides a successful model of the variations in angular momentum in the full model. The relevance of the results to James and James' finding ultralow-frequency variability in a five-layer model and to the possibility of ultralow-frequency variability in the atmosphere is discussed.

This paper revisits calculation of motion for a shallow-water barotropic vortex with fixed mean axisymmetric structure. The algorithm marches the linear primitive equations for the wavenumber 1 asymmetry forward in time using a vortex motion extrapolated from previous calculations. Periodically, it examines the calculated asymmetry for the apparent asymmetry due to mispositioning of the vortex center, repositions the vortex to remove the apparent asymmetry, and passes the corrected vortex motion on to the next cycle. This approach differs from the author's earlier variational determination of the steady-state motion after initial transients had died away. The steady-state approach demonstrated that the vortex had normal modes at zero frequency and, when an annulus of weak anticyclonic flow encircled the cyclonic inner vortex, at the most anticyclonic rotation frequency of the mean flow. Forcing of the former model led to too rapid steady-state poleward motion on a beta plane. At least for the linear problem, the key to more realistic simulation of motion and structure is the normal modes' transient response to diverse forcing: environmental potential vorticity gradients, embedded sources and sinks of mass, and initial asymmetries. The beta effect and other environmental potential vorticity gradients excite the normal modes to induce an acceleration of the vortex center toward and to the left of the direction to maximum environmental vorticity. Times approximates 100 days would be required to reach the too fast motions predicted in the earlier work. A rotating mass source-sink pair drives the vortex along a cycloidal track, but does not force the normal modes. A nonrotating source-sink forces a motion from the source toward the sink and excites the normal modes, leading to motion that persists after the forcing has ceased. Similarly, initial asymmetries that project onto the normal modes maintain themselves for times greater than or equal to 10 days, leading to persistent vortex propagation that evolves as the complex normal-mode frequencies dictate. Understanding of these normal modes can contribute to better tropical cyclone motion forecasts through better initialization of numerical track prediction models.

The two-revolving cluster model is based on a cascade of 11 gamma-rays forming a hyperdeformed band of (sup 152)(sub 66)Dy(86). The band ranges between 82-104 K for the angular-momentum quantum number. A pair of spheron tiers are found in the cluster p(13)n(18). The radii of revolution of the inner and outer tiers are 8.00 and 1.20 fm, respectively.

Byline: T. Makimae, T. Yamada, I. Yamaguchi, K. Takahashit In order to meet the demand for motor cars with reduced cost and weight, the bolts must be tightened more precisely and stably. Tightening techniques - the plastic region tightening method and the elastic region angle-controlled method, instead of the conventional toraue-controlled method - were studied and successfully applied to main engine parts. In addition to angle control with snug torque, seating point control was also developed, and both methods were applied to the plastic region tightening method. These methods were applied to elastic region angle control and resulted to high tightening quality in such ways as an improvement in separation load of connecting rod mating face and obtaining a proper clearance between the crankshaft journal and the metal.

Byline: Zhang Shihong, Z.R. Wang In this paper, the procedure and the principle of integral hydrobulge forming technology of spherical vessels and elastic-plastic stress distribution are described. Mechanical models of the angular distortion are set up. The hastening-sphere bending moment and the hastening-sphere effect of the angular distortion are explained.