Parallel Hamiltonian Formulation for Forward Dynamics of Free-Flying Manipulators

In previous work, a method for establishing the equations of motion of open-loop multibody mechanisms was introduced. The proposed forward dynamics formulation resulted in a Hamiltonian set of 2n first order ODE’s in the generalized coordinates q and the canonical momenta p. These Hamiltonian equations were derived from a recursive Newton-Euler formulation. It was shown how an O(n) formulation could be obtained in the case of a serial structure with general joints. The amount of required arithmetical operations was considerably less than comparable acceleration based formulations. In this paper, a further step is taken: the method is extended to constrained multibody systems. Using the principle of virtual power, it is possible to obtain a recursive Hamiltonian formulation for closed-loop mechanisms as well, enabling the combination of the low amount of arithmetical operations and a better evolution of the constraints violation errors, when compared with acceleration based methods.

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Hamiltonian Formulation Of Piano String Lagrangian Density With Riemann-Liouville Fractional Definition

10.36621/0397-005-002-017 ◽

2019 ◽

pp. 428

Author(s):

Emad Khaled Jaradat

Keyword(s):

Lagrangian Density ◽

Hamiltonian Formulation

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Hamiltonian Formulation Of Piano String Lagrangian Density With Riemann Liouville Fractional Definition

10.36621/0397-004-001-011 ◽

2018 ◽

pp. 259

Author(s):

Emad K. Jaradat

Keyword(s):

Lagrangian Density ◽

Hamiltonian Formulation

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Shape Dynamics and the Linking Theory

10.1093/oso/9780198789475.003.0012 ◽

2018 ◽

Author(s):

Flavio Mercati

Keyword(s):

Phase Space ◽

Degrees Of Freedom ◽

Line Element ◽

Hamiltonian Formulation ◽

Operational Definition ◽

Extended Phase Space ◽

Extended Phase ◽

Problem Of Time ◽

Definition Of ◽

Matter Fields

This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

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General Relativity

10.1093/oso/9780198822158.001.0001 ◽

2019 ◽

Cited By ~ 1

Author(s):

Steven Carlip

Keyword(s):

General Relativity ◽

High Energy Physics ◽

Hamiltonian Formulation ◽

Experimental Tests ◽

High Energy ◽

Gravitational Energy ◽

Field Equations ◽

Physics First ◽

Condensed Matter Theory ◽

Introductory Textbooks

This work is a short textbook on general relativity and gravitation, aimed at readers with a broad range of interests in physics, from cosmology to gravitational radiation to high energy physics to condensed matter theory. It is an introductory text, but it has also been written as a jumping-off point for readers who plan to study more specialized topics. As a textbook, it is designed to be usable in a one-quarter course (about 25 hours of instruction), and should be suitable for both graduate students and advanced undergraduates. The pedagogical approach is “physics first”: readers move very quickly to the calculation of observational predictions, and only return to the mathematical foundations after the physics is established. The book is mathematically correct—even nonspecialists need to know some differential geometry to be able to read papers—but informal. In addition to the “standard” topics covered by most introductory textbooks, it contains short introductions to more advanced topics: for instance, why field equations are second order, how to treat gravitational energy, what is required for a Hamiltonian formulation of general relativity. A concluding chapter discusses directions for further study, from mathematical relativity to experimental tests to quantum gravity.

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Currents, charges and algebras in exceptional generalised geometry

Journal of High Energy Physics ◽

10.1007/jhep06(2021)070 ◽

2021 ◽

Vol 2021 (6) ◽

Author(s):

David Osten

Keyword(s):

Current Algebra ◽

Hamiltonian Formulation ◽

Building Blocks ◽

Lie Derivative ◽

Consistency Check ◽

World Volume ◽

Invariant Currents ◽

Invariant Current ◽

M Theory ◽

A Current

Abstract A classical Ed(d)-invariant Hamiltonian formulation of world-volume theories of half-BPS p-branes in type IIb and eleven-dimensional supergravity is proposed, extending known results to d ≤ 6. It consists of a Hamiltonian, characterised by a generalised metric, and a current algebra constructed s.t. it reproduces the Ed(d) generalised Lie derivative. Ed(d)-covariance necessitates the introduction of so-called charges, specifying the type of p-brane and the choice of section. For p > 2, currents of p-branes are generically non- geometric due to the imposition of U-duality, e.g. the M5-currents contain coordinates associated to the M2-momentum.A derivation of the Ed(d)-invariant current algebra from a canonical Poisson structure is in general not possible. At most, one can derive a current algebra associated to para-Hermitian exceptional geometry.The membrane in the SL(5)-theory is studied in detail. It is shown that in a generalised frame the current algebra is twisted by the generalised fluxes. As a consistency check, the double dimensional reduction from membranes in M-theory to strings in type IIa string theory is performed. Many features generalise to p-branes in SL(p + 3) generalised geometries that form building blocks for the Ed(d)-invariant currents.

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A Simulation of the Effects of Badminton Serve Release Height

Applied Sciences ◽

10.3390/app11072903 ◽

2021 ◽

Vol 11 (7) ◽

pp. 2903

Author(s):

John Rasmussen ◽

Mark de Zee

Keyword(s):

Experimental Data ◽

Monte Carlo Simulation ◽

Monte Carlo ◽

World Federation ◽

Forward Dynamics ◽

Dynamics Model ◽

Rib Cage ◽

Female Player ◽

Ballistic Trajectory ◽

Release Height

In this work, we develop and calibrate a model to represent the trajectory of a badminton shuttlecock and use it to investigate the influence of serve height in view of a new serve rule instated by the Badminton World Federation. The new rule means that all players must launch the shuttlecock below a height of 1.15 m, as opposed to the old rule whereby the required launch height was under the rib cage of the server. The model is based on a forward dynamics model of ballistic trajectory with drag, and it is calibrated with experimental data. The experiments also served to determine the actual influence of the new rule on the shuttlecock launch position. The model is used in a Monte Carlo simulation to determine the statistical influence of the new serve rules on the player’s ability to perform good serves; i.e., serves with little opportunity for the receiver to attack. We conclude that, for the female player in question, serving below a height of 1.15 m makes it marginally more difficult to perform excellent serves. We also conclude that there might be alternative launch positions that would be less likely to produce the best serves but could be exploited as a tactical option.

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