Rotations and the Third Conservation Law: Angular Momentum

2015 ◽  
pp. 446-475
Keyword(s):  
Angular Momentum ◽  
Conservation Law ◽  
The Third

scholarly journals Explicit Overturning Limit of Rigid Block Using Triple and Pseudo-Triple Impulses Under Critical Near-Fault Ground Motions

2021 ◽  
Vol 7 ◽  
Author(s):  
Sae Homma ◽  
Kunihiko Nabeshima ◽  
Izuru Takewaki
Keyword(s):  
Angular Momentum ◽  
Conservation Law ◽  
Mechanical Energy ◽  
Rotational Velocity ◽  
Rigid Block ◽  
The Third ◽  
Maximum Angle ◽  
Critical Timing ◽  
The Impact ◽  
Angle Of Rotation

An explicit limit for the overturning of a rigid block is derived on the input level of the triple impulse and the pseudo-triple impulse as a modified version of the triple impulse that are a substitute of a near-fault forward-directivity ground motion. The overturning behavior of the rigid block is described by applying the conservation law of angular momentum and the conservation law of mechanical energy (kinetic and potential). The initial velocity of rotation after the first impulse and the change of rotational velocity after the impact on the floor due to the movement of the rotational center are determined by using the conservation law of angular momentum. The maximum angle of rotation after the first impulse is obtained by the conservation law of mechanical energy. The change of rotational velocity after the second impulse is also characterized by the conservation law of angular momentum. The maximum angle of rotation of the rigid block after the second impulse, which is mandatory for the computation of the overturning limit, is also derived by the conservation law of mechanical energy. This allows us to prevent from computing complex non-linear time-history responses. The critical timing of the second impulse (also the third impulse timing to the second impulse) is featured by the time of impact after the first impulse. As in the case of the double impulse, the action of the second impulse just after the impact is employed as the critical timing. It is induced from the explicit expression of the critical velocity amplitude limit of the pseudo-triple impulse that its limit is slightly larger than the limit for the double impulse. Finally, it is found that, when the third impulse in the triple impulse is taken into account, the limit input velocity for the overturning of the rigid block becomes larger than that for the pseudo-triple impulse. This is because the third impulse is thought to prevent the overturning of the rigid block by giving an impact toward the inverse direction of the vibration of the rigid block.

“The Chords of the German Soul are Tuned to Nature”: The Movement to Preserve the Natural Heimat from the Kaiserreich to the Third Reich

1996 ◽  
Vol 29 (3) ◽  
pp. 339-384 ◽  
Author(s):  
John Alexander Williams
Keyword(s):  
Weimar Republic ◽  
Conservation Law ◽  
Third Reich ◽  
Natural Community ◽  
The Third ◽  
The Past ◽  
Hard Times ◽  
The Third Reich ◽  
German People ◽  
State Protection

In the early 1930s, Dr. Konrad Guenther, a longtime advocate of nature conservation, was exhorting the German people to return to “the soil of the homeland.” In the past, according to Guenther, whenever the German people had been forced to respond vigorously to the pressure of hard times, they had returned to their “natural” roots. He called on the population to learn about the Heimat (homeland) and its natural environment, ‘not only through reason alone, but with the entire soul and personality; for the chords of the German soul are tuned to nature. Let us allow nature to speak, and let us be happy to be German!” The stakes were high, for if the German people failed in this way to unite into a strong, “natural” community, they would become “cultural fertilizer for other nations.” Following the fall of the Weimar Republic and the Nazi seizure of power in 1933, Guenther became one of the most vocal exponents of the notion that conserving nature would aid in the cultural unification and “racial cleansing” of Germany. Indeed, Guenther and his fellow conservationists saw their longstanding dream of a nationwide conservation law at last fulfilled under the Third Reich. The 1935 Reich Conservation Law guaranteed state protection of “the nature of the Heimat in all its manifestations”—if necessary through police measures.

scholarly journals Partial conservation law in a schematic single j shell model

2017 ◽  
Vol 26 (01n02) ◽  
pp. 1740021 ◽  
Author(s):  
Wesley Pereira ◽  
Ricardo Garcia ◽  
Larry Zamick ◽  
Alberto Escuderos ◽  
Kai Neergård
Keyword(s):  
Angular Momentum ◽  
Matrix Element ◽  
Shell Model ◽  
Linear Function ◽  
Conservation Law ◽  
Interaction Matrix ◽  
Stationary States ◽  
Interaction Matrix Element ◽  
Angular Momenta ◽  
Partial Conservation

We report the discovery of a partial conservation law obeyed by a schematic Hamiltonian of two protons and two neutrons in a [Formula: see text] shell. In our Hamiltonian, the interaction matrix element of two nucleons with combined angular momentum [Formula: see text] is linear in [Formula: see text] for even [Formula: see text] and constant for odd [Formula: see text]. It turns out that in some stationary states, the sum of the angular momenta [Formula: see text] and [Formula: see text] of the proton and neutron pairs is conserved. The energies of these states are given by a linear function of [Formula: see text]. The systematics of their occurrence is described and explained.

Conservation Principles for Systems With a Varying Number of Degrees-of-Freedom

1998 ◽  
Vol 65 (3) ◽  
pp. 719-726 ◽  
Author(s):  
S. Djerassi
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Linear Momentum ◽  
Dynamical Equations ◽  
The Third ◽  
Conservation Principles

This paper is the third in a trilogy dealing with simple, nonholonomic systems which, while in motion, change their number of degrees-of-freedom (defined as the number of independent generalized speeds required to describe the motion in question). The first of the trilogy introduced the theory underlying the dynamical equations of motion of such systems. The second dealt with the evaluation of noncontributing forces and of noncontributing impulses during such motion. This paper deals with the linear momentum, angular momentum, and mechanical energy of these systems. Specifically, expressions for changes in these quantities during imposition and removal of constraints are formulated in terms of the associated changes in the generalized speeds.

Sustainability and Marine Conservation Law

2020 ◽  
pp. 213-236
Author(s):  
Margherita Pieraccini
Keyword(s):  
Conservation Law ◽  
Marine Conservation ◽  
Habitats Directive ◽  
Natural Habitats ◽  
Trade Off ◽  
Agenda 2030 ◽  
The Third ◽  
Wild Fauna ◽  
Council Directive ◽  
Point Of Departure

This chapter takes at its point of departure SDG 14 (life below water) and the specific target of conservation (SDG 14.5). It shows that interpreting SDG 14.5 within the context and purpose of Agenda 2030 means paying attention to three main sustainability criteria. The first relates to substantive socio-ecological inter-pillar relationality, that is to say an acknowledgement of ontological relationality between pillars, beyond an understanding of sustainability as trade off. The second relates to intra-pillar relationality, that is links between conservation and other environmental sectors and the third to procedural inclusion through participatory decision-making in line with the epistemic pluralisation of sustainability. These three criteria are used to assess the sustainability of current EU marine conservation law. One legislative instrument on marine conservation in EU law is chosen as example, namely the Council Directive 92/43/EEC of 21 May 1992 on the conservation of natural habitats and of wild fauna and flora. The Habitats Directive is the cornerstone of conservation law in the EU and it is among the instruments listed by the European Commission as ways to support the implementation of Agenda 2030 and target 14.5.

Angular momentum in general relativity I. Definition and asymptotic behaviour

1977 ◽  
Vol 354 (1679) ◽  
pp. 379-405 ◽  
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Angular Momentum ◽  
Asymptotic Behaviour ◽  
Event Horizon ◽  
Conservation Law ◽  
General Definition ◽  
Field Equations ◽  
Spin Coefficient ◽  
Coefficient Formalism

Angular momentum in axisymmetric space-times is investigated. The conclusions lead to a general definition suitable for all asymptoticallyflat spaces which is valid both at infinity and on the event horizon of a black hole. This first paper restricts attention to considerations at infinity. Working in terms of the spin coefficient formalism, the field equations are solved asymptotically at large distances and the definition is evaluated. A conservation law is derived and finally the effect on the angular momentum of a supertranslation of the coordinates is discussed.

Periodic Orbits of Radially Symmetric Systems with a Singularity: the Repulsive Case

2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Alessandro Fonda ◽  
Rodica Toader
Keyword(s):  
Angular Momentum ◽  
Periodic Orbits ◽  
Large Amplitude ◽  
Topological Degree ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
Periodic Forcing ◽  
The Third ◽  
Large Angular Momentum ◽  
Symmetric Systems

AbstractWe study radially symmetric systems with a singularity of repulsive type. In the presence of a radially symmetric periodic forcing, we show the existence of three distinct families of subharmonic solutions: One oscillates radially, one rotates around the origin with small angular momentum, and the third one with both large angular momentum and large amplitude. The proofs are carried out by the use of topological degree theory.

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