Related papers: The Hyperbolic Tangent as an Educational Tool for …
This paper outlines a deceptively complex problem in classical mechanics which the paper names the "Falling Astronaut Problem," and it explores a method for teachers to implement this problem in an undergraduate classroom. The paper…
This paper provides a simplified explanation of the vacuum bazooka through diagrams and builds a theoretical model only using concepts found in introductory mechanics. Our theory suggests that the velocity of the projectile is proportional…
Real-time accurate solutions of large-scale complex dynamical systems are in critical need for control, optimization, uncertainty quantification, and decision-making in practical engineering and science applications, especially digital twin…
The objective of this paper is to provide a pedagogical framework for the phenomenon of orbital decay of satellites in low Earth orbit. The dynamics of orbital decay are derived considering atmospheric drag as the only dissipative mechanism…
In the study, analyzes were made for one-dimensional constant acceleration motion using the Arduino microcontroller and distance sensor, using the position and time values obtained for the movement of an object thrown from bottom to top…
This paper reports the use of Tracker as a pedagogical tool in supporting effective learning and teaching of toss up and free fall motion for beginning grade 9 students. This is a case study with (N=123) students of express-pure physics…
Hyperbolic tangent and Sigmoid functions are used as non-linear activation units in the artificial and deep neural networks. Since, these networks are computationally expensive, customized accelerators are designed for achieving the…
We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this…
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…
From the mesoscopic point of view, a new concept of soft matching for mass points is proposed. Then a soft Lasso's approach to learn the soft dynamical equation for the physical mechanical relationship is proposed, too. Furthermore, a…
In this work we discuss in detail the known solutions of the stationary Schr\"odinger equation subject to a deformable hyperbolic tangent potential exactly soluble $ V(x) = \frac {V_0} {2} (1+ \tanh (\delta x)) $. We find the analytical…
In this paper, we use variational minimizing method to prove the existence of hyperbolic solution with a prescribed positive energy for N-body type problems with strong forces. Firstly, we get periodic solutions using suitable constraints,…
This workshop aims to demonstrate how the Tracker Video Analysis and Modeling Tool engages, enables and empowers teachers to be learners so that we can be leaders in our teaching practice. Through this workshop, the kinematics of a falling…
This paper presents and experimentally demonstrates a novel framework for variable assistance on lower body exoskeletons, based upon safety-critical control methods. Existing work has shown that providing some freedom of movement around a…
Gradient descent generalises naturally to Riemannian manifolds, and to hyperbolic $n$-space, in particular. Namely, having calculated the gradient at the point on the manifold representing the model parameters, the updated point is obtained…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider a model for spin-orbital motion: orbital…
A new variational technique determines the general condition of equilibrium of a rotating gravito-electromagnetic system and provides a modified dynamical equation of motion from where it emerges a so-far unforseen topological torsion…
Despite recent advances in robust locomotion, bipedal robots operating in the real world remain at risk of falling. While most research focuses on preventing such events, we instead concentrate on the phenomenon of falling itself.…
We discuss several explicitly causal hyperbolic formulations of Einstein's dynamical 3+1 equations in a coherent way, emphasizing throughout the fundamental role of the ``slicing function,'' $\alpha$---the quantity that relates the lapse…
The existence of hyperbolic orbits is proved for a class of restricted three-body problems with a fixed energy by taking limit for a sequence of periodic solutions which are obtained by variational methods.