Related papers: Double pendulum model for tennis stroke including …
We establish a general formula for the distribution of the score in table tennis. We use this formula to derive the probability distribution (and hence the expectation and variance) of the number of rallies necessary to achieve any given…
A new kinetic model is proposed where the equilibrium distribution with bounded support has a range of velocities about two average velocities in 1D. In 2D, the equilibrium distribution function has a range of velocities about four average…
Polymer entanglements lead to complicated topological constraints and interactions between neighbouring chains in a dense solution or melt. Entanglements can be treated in a mean field approach, within the famous reptation model, since they…
Achieving versatile and explosive motion with robustness against dynamic uncertainties is a challenging task. Introducing parallel compliance in quadrupedal design is deemed to enhance locomotion performance, which, however, makes the…
A Newton's cradle is a device that demonstrates conservation of momentum using a series of identical colliding pendula. Despite being a famous example that demonstrates the concept of momentum conservation, extensive analysis of the system…
A model of two oscillating pendula placed on a mobile support is studied. Once an overall scheme of equations, under general assumptions, is formulated via the Lagrangian equations of motion, the specific case of absence of escapement is…
The double pendulum, a simple system of classical mechanics, is widely studied as an example of, and testbed for, chaotic dynamics. In 2016, Maiti et al. studied a generalization of the simple double pendulum with equal point-masses at…
Numerical experiments of the statistical evolution of an ensemble of non-interacting particles in a time-dependent billiard with inelastic collisions, reveals the existence of three statistical regimes for the evolution of the speeds…
Tennis is one of the world's biggest and most popular sports. Multiple researchers have, with limited success, modeled the outcome of matches using probability modelling or machine learning approaches. The approach presented here predicts…
In this paper, numerical estimation of frictional torques is carried out of a rotary elastic disc on a hard and rough surface under different rotating conditions. A one dimensional spring- mass rotary system is numerically solved under the…
Training diffusion models is always a computation-intensive task. In this paper, we introduce a novel speed-up method for diffusion model training, called, which is based on a closer look at time steps. Our key findings are: i) Time steps…
We apply methods of the so-called `inverse problem of the calculus of variations' to the stabilization of an equilibrium of a class of two-dimensional controlled mechanical systems. The class is general enough to include, among others, the…
Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical systems theory. In particular, the double pendulum is a prototypical chaotic system that is frequently used to…
In this contribution, a new class of lattice Boltzmann schemes is introduced and studied. These schemes are presented in a framework that generalizes the multiple relaxation times method of d'Humi\`eres. They extend also the Geier's…
In tennis tournaments, momentum, a critical yet elusive phenomenon, reflects the dynamic shifts in performance of athletes that can decisively influence match outcomes. Despite its significance, momentum in terms of effective modeling and…
Bipedal locomotion is a phenomenon that still eludes a fundamental and concise mathematical understanding. Conceptual models that capture some relevant aspects of the process exist but their full explanatory power is not yet exhausted. In…
An adjoint-based optimization is applied to study the thrust performance of a pitching-rolling ellipsoidal plate in a uniform stream at Reynolds number 100. To achieve the highest thrust, the optimal kinematics of pitching-rolling motion is…
Momentum methods for convex optimization often rely on precise choices of algorithmic parameters, based on knowledge of problem parameters, in order to achieve fast convergence, as well as to prevent oscillations that could severely…
In this paper we study the system of two falling balls in continuous time. We modell the system by a suspension flow over a two dimensional, hyperbolic base map. By detailed analysis of the geometry of the system we identify special…
This study introduces lateral pendulum as an innovative balancer design for bicycle stabilization. This pendulum, operating in the bicycle's vertical plane, enables the bicycle to remain stationary. The paper develops a dynamic model for a…