Mathematical survey of the action principle

2021 ◽  
Vol 15 (3) ◽  
pp. 101-106
Author(s):  
Hans Detlef Hüttenbach
Keyword(s):  
Action Principle

VARIATIONAL OPTIMUM ACTION PRINCIPLE

2019 ◽  
Vol 7 (67) ◽  
Author(s):  
V. V. Nikitin
Keyword(s):  
Action Principle

scholarly journals Non-Riemannian gravity actions from double field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
A. D. Gallegos ◽  
U. Gürsoy ◽  
S. Verma ◽  
N. Zinnato
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Condensed Matter ◽  
Equations Of Motion ◽  
Technical Note ◽  
Action Principle ◽  
Relativistic Symmetry ◽  
Gravitational Theories ◽  
Double Field Theory

Abstract Non-Riemannian gravitational theories suggest alternative avenues to understand properties of quantum gravity and provide a concrete setting to study condensed matter systems with non-relativistic symmetry. Derivation of an action principle for these theories generally proved challenging for various reasons. In this technical note, we employ the formulation of double field theory to construct actions for a variety of such theories. This formulation helps removing ambiguities in the corresponding equations of motion. In particular, we embed Torsional Newton-Cartan gravity, Carrollian gravity and String Newton-Cartan gravity in double field theory, derive their actions and compare with the previously obtained results in literature.

scholarly journals A least action principle for interceptive walking

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun Chae Chung ◽  
MooYoung Choi
Keyword(s):  
Social Systems ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Action Principle ◽  
Lagrange Equations ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Human Participants

AbstractThe principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

scholarly journals Action principle for the fluid-gravity correspondence and emergent gravity

2012 ◽  
Vol 85 (2) ◽  
Author(s):  
Sanved Kolekar ◽  
T. Padmanabhan
Keyword(s):  
Action Principle ◽  
Emergent Gravity

scholarly journals Actions, topological terms and boundaries in first-order gravity: A review

2016 ◽  
Vol 25 (04) ◽  
pp. 1630011 ◽  
Author(s):  
Alejandro Corichi ◽  
Irais Rubalcava-García ◽  
Tatjana Vukašinac
Keyword(s):  
Boundary Conditions ◽  
Symplectic Structure ◽  
Equations Of Motion ◽  
Hamiltonian Formalism ◽  
Action Principle ◽  
Internal Boundary ◽  
Four Dimensions ◽  
First Order ◽  
Conserved Charges ◽  
Boundary Terms

In this review, we consider first-order gravity in four dimensions. In particular, we focus our attention in formulations where the fundamental variables are a tetrad [Formula: see text] and a [Formula: see text] connection [Formula: see text]. We study the most general action principle compatible with diffeomorphism invariance. This implies, in particular, considering besides the standard Einstein–Hilbert–Palatini term, other terms that either do not change the equations of motion, or are topological in nature. Having a well defined action principle sometimes involves the need for additional boundary terms, whose detailed form may depend on the particular boundary conditions at hand. In this work, we consider spacetimes that include a boundary at infinity, satisfying asymptotically flat boundary conditions and/or an internal boundary satisfying isolated horizons boundary conditions. We focus on the covariant Hamiltonian formalism where the phase space [Formula: see text] is given by solutions to the equations of motion. For each of the possible terms contributing to the action, we consider the well-posedness of the action, its finiteness, the contribution to the symplectic structure, and the Hamiltonian and Noether charges. For the chosen boundary conditions, standard boundary terms warrant a well posed theory. Furthermore, the boundary and topological terms do not contribute to the symplectic structure, nor the Hamiltonian conserved charges. The Noether conserved charges, on the other hand, do depend on such additional terms. The aim of this manuscript is to present a comprehensive and self-contained treatment of the subject, so the style is somewhat pedagogical. Furthermore, along the way, we point out and clarify some issues that have not been clearly understood in the literature.

scholarly journals Action principle for action-dependent Lagrangians toward nonconservative gravity: Accelerating universe without dark energy

2017 ◽  
Vol 95 (10) ◽  
Author(s):  
Matheus J. Lazo ◽  
Juilson Paiva ◽  
João T. S. Amaral ◽  
Gastão S. F. Frederico
Keyword(s):  
Dark Energy ◽  
Action Principle ◽  
Accelerating Universe

The action principle of organic plasticizers in cement suspensions determined from centrifugation

2013 ◽  
Vol 34 (9) ◽  
pp. 1483-1488 ◽  
Author(s):  
Gordana Paravanova ◽  
Berenika Hausnerova ◽  
Juan Carlos Beltrán Prieto
Keyword(s):  
Action Principle

scholarly journals Phase reconstruction by the weighted least action principle

2006 ◽  
Vol 8 (3) ◽  
pp. 279-289 ◽  
Author(s):  
Chungmin Lee ◽  
John Lowengrub ◽  
Jacob Rubinstein ◽  
Xiaoming Zheng
Keyword(s):  
Action Principle ◽  
Phase Reconstruction ◽  
Least Action Principle ◽  
Least Action
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