Indentation of an elastic disk on a circular supporting ringThin elastic two-dimensionnal systems under compressive stresses may relieve part of their stretching energy by developing out of plane undulations. We investigate experimentally and theoretically…Tristan Suzanne, Julien Deschamps, Marc Georgelin et al.·Jul 7, 2022SaveLearn
Open system control of dynamical transitions under the generalized Kruskal-Neishtadt-Henrard theoremUseful dynamical processes often begin through barrier-crossing dynamical transitions; engineering system dynamics in order to make such transitions reliably is therefore an important task for…Diego M. Fieguth, James R. Anglin·Jul 6, 2022SaveLearn
Singular Lagrangians and the Dirac--Bergmann Algorithm in Classical MechanicsTextbook treatments of classical mechanics typically assume that the Lagrangian is nonsingular. That is, the matrix of second derivatives of the Lagrangian with respect to the velocities is…J. David Brown·Jun 30, 2022SaveLearn
Space pirates: a pursuit curve problem involving retarded timeWe revisit the classical pursuit curve problem solved by Pierre Bouguer in the 18th century, taking into account that information propagates at a finite speed. To a certain extent, this could be seen…Thales Azevedo, Anderson Pelluso·Jun 29, 2022SaveLearn
A Worked Example of the Bayesian Mechanics of Classical ObjectsBayesian mechanics is a new approach to studying the mathematics and physics of interacting stochastic processes. Here, we provide a worked example of a physical mechanics for classical objects,…Dalton A R Sakthivadivel·Jun 27, 2022SaveLearn
Unveiling the physics of partial differential equations with heuristicsHeuristic arguments and order of magnitude estimates for partial differential equations highlight essential features of the physics they describe. We present order of magnitude estimates, and their…Valerio Faraoni·Jun 24, 2022SaveLearn
Wigner rotation and Euler angle parametrizationAnalogous to the famous Euler angle parametrization in three-dimensional Euclidean space, a reflection-free Lorentz transformation in (2+1)-dimensional Minkowski space can be decomposed into three…Leehwa Yeh·Jun 22, 2022SaveLearn
Kramers-Kronig relations and the analogy between electromagnetic and mechanical wavesThe important consequence of the Kramers-Kronig relations (KKrs) is that dissipative behavior in material media inevitably implies the existence of dispersion, i.e., a frequency dependence in the…J. Carcione, F. Mainardi, J. Ba et al.·Jun 22, 2022SaveLearn
A modified Bragg's law of Class I Bragg resonances of linear long waves excited by an array of artificial barsBased on the band theory of Bloch waves, a modified Bragg's law is established for Class I Bragg resonances when linear long waves are reflected by a finite periodic array of artificial bars,…Huan-Wen Liu·Jun 20, 2022SaveLearn
Swinging a playground swing: torque controls for inducing sustained oscillationsModels of a playground swing have been studied since the 1960s. However, in most of them, the position of the swinger is controlled directly. This simplifies the problem but hides the mechanics of…Sergiy Koshkin, Vojin Jovanovic·Jun 20, 2022SaveLearn
Anomalous curvature evolution and geometric regularization of energy focusing in the snapping dynamics of a flexible bodyWe examine the focusing of kinetic energy and the amplification of various quantities during the snapping motion of the free end of a flexible structure. This brief but violent event appears to be a…A. R. Dehadrai, J. A. Hanna·Jun 16, 2022SaveLearn
Deterministic and Random Perturbations of the Kepler ProblemWe investigate perturbations in the Kepler problem. We offer an overview of the dynamical system using Newtonian, Lagrangian and Hamiltonian Mechanics to build a foundation for analyzing…Jesse Dimino·Jun 15, 2022SaveLearn
Complex Spatiotemporal Modulations and Non-Hermitian Degeneracies in PT-Symmetric Phononic MaterialsUnraveling real eigenfrequencies in non-Hermitian PT-symmetric Hamiltonians has opened new avenues in quantum physics, photonics, and most recently, phononics. However, the existing…M. Moghaddaszadeh, M. A. Attarzadeh, A. Aref et al.·Jun 11, 2022SaveLearn
Formulations of the Elastodynamic Equations in Anisotropic and Multiphasic Porous Media from the Principle of Energy ConservationElastodynamic equations have been formulated with either Newton's second law of motion, Lagrange's equation, or Hamilton's principle for over 150 years. In this work, contrary to…Yinqiu Zhou, Xiumei Zhang, Lin Liu et al.·Jun 9, 2022SaveLearn
Design of electrostatic feedback for an experiment to measure GThe torsion pendulum at the heart of the apparatus to measure the gravitational constant, G at the Bureau International des Poids et Mesures (BIPM) is used to measure the gravitational torque…Stephan Schlamminger, Leon Chao, Vincent Lee et al.·Jun 8, 2022SaveLearn
Upper bounds estimates of the distance to cubic or orthotropic elasticityWe address the problem, not of the determination -- which usually needs numerical methods -- but of an accurate analytical estimation of the distance of a raw elasticity tensor to cubic symmetry and…Rodrigue Desmorat, Boris Kolev·Jun 7, 2022SaveLearn
Projectile motion in a medium with quadratic drag at constant horizontal windA classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account with the use of the quadratic resistance law. The action of…Peter Chudinov·Jun 6, 2022SaveLearn
Creep in Rotating Composite Disk having Variable Thickness Subjected to Thermal as well as Particle GradientThe motivation behind this paper is to present the effect of thermal and particle gradient in rotating composite disk with variable thickness using Sherby law. The values of tangential, radial…Harjot Kaur, Nishi Gupta, Anjali Jain·Jun 1, 2022SaveLearn
From elasticity tetrads to rectangular vielbeinThe paper is devoted to the memory of Igor E. Dzyaloshinsky. In our common paper I.E. Dzyaloshinskii and G.E. Volovick, Poisson brackets in condensed matter, Ann. Phys. 125 67--97 (1980), we…G. E. Volovik·May 30, 2022SaveLearn
Elimination of Pathological Solutions of the Abraham-Lorentz Equation of MotionFor more than a century the Abraham-Lorentz equation has generally been regarded as the correct description of the dynamics of a charged particle. However, there are pathological solutions of the…Anupam Shaw·May 30, 2022SaveLearn
The vibrational modes of simplicial moleculesConsider a "simplicial molecule": n equal point masses placed at the vertices of a regular (n-1)-simplex, connected by n 2 identical springs. We apply the representation…Charles H. Conley, Jon Erickson·May 30, 2022SaveLearn
On the reduction of nonlinear electromechanical systemsThe present work revisits the reduction of the nonlinear dynamics of an electromechanical system through a quasi-steady state hypothesis, discussing the fundamental aspects of this type of approach…Americo Cunha, Marcelo Pereira, Rafael Avanço et al.·May 27, 2022SaveLearn
Conformal optical black hole for cavityWhispering gallery mode (WGM) cavity is important for exploring physics of strong light-matter interaction. Yet it suffers from the notorious radiation loss universally due to the light tunneling…Qingtao Ba, Yangyang Zhou, Jue Li et al.·May 22, 2022SaveLearn
Self radiation force on a moving monopolar sourceThe radiation force exerted on an object by an acoustic wave is a widely studied phenomenon since the early work of Rayleigh, Langevin and Brillouin and has led in the last decade to tremendous…Aymeric Roux, Jean-Paul Martishang, Michael Baudoin·May 19, 2022SaveLearn
When action is not least for systems with action-dependent LagrangiansThe dynamics of some non-conservative and dissipative systems can be derived by calculating the first variation of an action-dependent action, according to the variational principle of Herglotz. This…Joseph Ryan·May 18, 2022SaveLearn