More than a century before quantum mechanics was born, Irish mathematician William Rowan Hamilton stumbled onto an idea that would quietly foreshadow one of the deepest truths in physics. While ...

Abstract: We address the development of a unified approach for the necessary conditions for optimization of a functional arising in calculus of variations. In particular, we develop a unified approach ...

In the context of the Lagrangian and Hamiltonian mechanics, a generalized theory of coordinate transformations is analyzed. On the basis of such theory, a misconception concerning the superiority of ...

Physics and Python stuff. Most of the videos here are either adapted from class lectures or solving physics problems. I really like to use numerical calculations without all the fancy programming ...

The usual Lagrange equations of motion cannot be directly applied to systems with mass varying explicitly with position. In this particular context, a naive application, without any special ...

SC24-W: Workshops of the International Conference for High Performance Computing, Networking, Storage and Analysis Computational scientists often face challenges when developing and optimizing code ...

Abstract: The Euler equations with gravity are the foundation of dynamical cores of atmosphere, ocean, and cloud resolving models used in climate and weather prediction. A major challenge arises from ...

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...

Power and Flow Group, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands Eindhoven Institute for Renewable Energy Systems (EIRES ...

Department of Applied Physics, Tafila Technical University, Tafila, Jordan. Nonholonomic mechanics refers to the mechanical systems that are subject to constraints on the velocities. This mechanics is ...