Related papers: Projectile motion without calculus
We propose a novel foundation for calculus that focuses on the notion of approximations while avoiding the use of limits altogether. Continuity is defined as approximation at a point, while differentiability is defined as approximation with…
We propose a model of a learning agent whose interaction with the environment is governed by a simulation-based projection, which allows the agent to project itself into future situations before it takes real action. Projective simulation…
The existence of radial solutions of a nonlinear Dirichlet problem in a ball is translated to the language of Mechanics, i.e. to requirements on the time of motion of a particle in an external potential and under the action of a viscosity…
From the simple Lagrangian the equations of motion for the particle with spin are derived. The spin is shown to be conserved on the particle world-line. In the absence of a spin the equation coincides with that of a geodesic. The equations…
We study the dynamics of classical and quantum particles with spin and dipole moments in external fields within the framework of the general approach by making use of the projection technique. Applications include the neutrino physics in…
The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. The book begins with a brief review of relativity,…
The quantum mechanical motion of a relativistic particle in a non-continuous spacetime is investigated. The spacetime model is a dense, rationale subset of two-dimensional Minkowski spacetime. Solutions of the Dirac equation are calculated…
We discuss a role of a momentum vector in the description of dynamics of systems with variable mass, and show some ambiguity in expressing the 2nd Newtonian law of dynamics in terms of momentum change in time for variable-mass systems. A…
We introduce a model detector which registers the passage of a particle through the detector location, without substantially perturbing the particle wave function. (The exact time of passage is not determined in such measurements.) We then…
The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. The book begins with a brief review of relativity,…
The capability of making explainable inferences regarding physical processes has long been desired. One fundamental physical process is object motion. Inferring what causes the motion of a group of objects can even be a challenging task for…
This is a short introduction of the exterior form formalism focus on its applications in physics and then mostly aimed to physics students. As a rule of a game played here we never use a coordinate frame neither in the definitions nor in…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schroedinger equation or complex wavefunctions. Unlike the standard…
Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…
The multiplicative (or geometric) calculus is a non-Newtonian calculus derived from an arithmetic in which the operations of addition/subtraction/multiplication are replaced by multiplication/division/exponentiation. A major difference…
Our experiments and molecular dynamics simulations on a projectile penetrating a two-dimensional granular medium reveal that the mean deceleration of the projectile is constant and proportional to the impact velocity. Thus, the time taken…
In this work we study partial differential equations defined in a domain that moves in time according to the flow of a given ordinary differential equation, starting out of a given initial domain. We first derive a formulation for a…
The influence of the force of the quadratic resistance of the medium on the change in some interesting characteristics of the motion of the projectile, which take place when the projectile moves in vacuum, is investigated. Loci that ensure…
You will find here a number of (mostly) elementary physics problems dealing mainly with uniform motion kinematics. In preparing this collection I have tried to create original situations that could help bring motivation to an introductory…
We describe the development of a junior-senior level course for Physics majors designed to teach Mathematica skills in support of their undergraduate coursework, but also to introduce students to modern research level results. Standard…