Related papers: Projectile motion without calculus
The notion from ab-initio molecular dynamics simulations that nuclear motion is best described by classical Newton dynamics instead of the time-dependent Schr{\"o}dinger equation is substantiated. In principle a single experiment should…
During the process of teaching the concept of derivative, it is common and natural to refer to geometric interpretations, such as the use of the tangent line and the maximum and minimum points of a function, to illustrate the scope of the…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
Diffusion models have risen as a powerful tool in robotics due to their flexibility and multi-modality. While some of these methods effectively address complex problems, they often depend heavily on inference-time obstacle detection and…
This paper addresses the problem of planning a safe (i.e., collision-free) trajectory from an initial state to a goal region when the obstacle space is a-priori unknown and is incrementally revealed online, e.g., through line-of-sight…
Parametrized motion planning algorithms have high degrees of universality and flexibility, as they are designed to work under a variety of external conditions, which are viewed as parameters and form part of the input of the underlying…
A priority of physics instruction is to help students make the connection between the formulae they think they are required to memorize and the real world in which they interact every day. If you ask students to describe a situation in real…
We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
The small angle approximation often fails to explain experimental data, does not even predict if a plane pendulum's period increases or decreases with increasing amplitude. We make a perturbation ansatz for the Conserved Energy Surfaces of…
Planar run-and-tumble walks with orthogonal directions of motion are considered. After formulating the problem with generic transition probabilities among the orientational states, we focus on the symmetric case, giving general expressions…
We'll be presenting an approach to solve the equation of simple harmonic motion (SHM) which is non-standard as compared with the usual way of solution presented in textbooks. In addition to help students avoid the unnecessary memorization…
This essay is an attempted to address, from a modern perspective, the motion of a particle. Quantum mechanically, motion consists of a series of localizations due to repeated interactions that, taken close to the limit of the continuum,…
In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
As a profound example of spontaneous motion, we analyze the motion of a camphor particle on a water surface. The motion is modeled as an initial-boundary value problem for a coupled nonlinear system of a diffusion equation and an ordinary…
Recent differentiable rendering techniques have become key tools to tackle many inverse problems in graphics and vision. Existing models, however, assume steady-state light transport, i.e., infinite speed of light. While this is a safe…
Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today.…
Previous research has shown that students often struggle to develop an understanding of linear and quadratic relationships. Covariational reasoning has been identified as a way to support this development. This study aims to investigate how…