Related papers: The optimal angle of Release in Shot Put
This paper studies the time optimal control problem for systems of heat equations coupled by a pair of constant matrices. The control constraint is of the ball-type, while the target is the origin of the state space. We obtain an upper…
In this study, we propose an optimal assistive control strategy that uses estimated user's movement intention as the terminal cost function. We estimate the movement intention by observing human user's joint angle, angluar velocity, and…
Consider a random $d$-dimensional simplex whose vertices are $d+1$ random points sampled independently and uniformly from the unit sphere in $\mathbb R^d$. We show that the expected sum of solid angles at the vertices of this random simplex…
World records in athletics provide a measure of physical as well as physiological human performance. Here we analyse running records and show that the mean speed as a function of race time can be described by two scaling laws that have a…
The purpose of this research is to create a machine learning-based smart coaching approach for football that can replace manual analysis with real-time feedback for trainers. In-depth analysis of football player data by humans is…
Radiative coolers that can passively cool objects by radiating heat into the outer space have recently received much attention. However, the ultimate limits of their performance as well as their ideal spectral design are still unknown. We…
Model rockets have been employed in student projects, but very few papers in aerospace education offer concise summaries of activities at university-course levels. This paper aims to address this gap in the literature. The rockets used by…
Kiiking is an extreme sport in which athletes alternate between standing and squatting to pump a standing swing till it is inverted and completes a rotation. A minimal model of the sport may be cast in terms of the control of an actively…
We characterize the largest point sets in the plane which define at most 1, 2, and 3 angles. For $P(k)$ the largest size of a point set admitting at most $k$ angles, we prove $P(2)=5$ and $P(3)=5$. We also provide the general bounds of $k+2…
Using a portable star tracking system, we are able to obtain the geographical position of the observer, longitude, latitude and North direction. In this work, a new optimization method has been applied to improve accuracy in calculation of…
We study the estimation of the reach, an ubiquitous regularity parameter in manifold estimation and geometric data analysis. Given an i.i.d. sample over an unknown $d$-dimensional $\mathcal{C}^k$-smooth submanifold of $\mathbb{R}^D$, we…
We theoretically investigate the apparent contact angle and contact angle hysteresis of a droplet placed on a liquid infused surface. We show that the apparent contact angle is not uniquely defined by material parameters, but also has a…
Spin plays a pivotal role in ball-based sports. Estimating spin becomes a key skill due to its impact on the ball's trajectory and bouncing behavior. Spin cannot be observed directly, making it inherently challenging to estimate. In table…
Interplay of the angle dependent X-ray reflectivity and absorption with the photoelectron attenuation length in the photoelectron emission process determine the optimal X-ray incidence angle which maximizes the photoelectron signal.…
A planar point set is in convex position precisely when it has a convex polygonization, that is, a polygonization with maximum interior angle measure at most \pi. We can thus talk about the convexity of a set of points in terms of the…
In this paper, the current best estimate of a fundamental Galactic parameter Galactocentric distance of the Sun $R_0$ has been evaluated using all the available estimates published during the last 20 years. Unlike some other studies, our…
In this article, we study the behaviour of a looped string launched in ambient air using motorised wheels. We show that the loop, once it reaches its stationary state, is either in the pulley or the air-lifted state. The transition between…
In this paper, we investigate a pursuit-evasion game in which a mobile observer tries to track a target in an environment containing obstacles. We formulate the game as an optimal control problem with state inequality constraint in a simple…
We describe a randomized algorithm that, given a set $P$ of points in the plane, computes the best location to insert a new point $p$, such that the Delaunay triangulation of $P\cup\{p\}$ has the largest possible minimum angle. The expected…
The reported alignment between the projected spin-axes and proper motion directions of pulsars is revisited in the light of new data from Jodrell Bank and Effelsberg. The present investigation uses 54 pulsars, the largest to date sample of…