Related papers: A Qualitative Analysis to Simple Harmonic Motion
This paper presents and proves an equation for the time horizon of symmetric trajectories with zero boundary conditions and bounded derivatives of arbitrary order. This equation holds regardless of the number of phases comprising the…
An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the…
Waves in excitable media can be treated by a simple geometric theory. The propagation velocity is assumed known and evolution of wave fronts is determined by elementary physical principles (Fermat's principle, Huygens' principle). Based on…
Neuromuscular disorders, such as Spinal Muscular Atrophy (SMA) and Duchenne Muscular Dystrophy (DMD), cause progressive muscular degeneration and loss of motor function for 1 in 6,000 children. Traditional upper limb motor function…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
We consider a class of "harmonic variations" for nonsingular curves, obtained as asymptotic degenerations along bitangents. On a geometric level, we obtain an attractive relationship between the class and the genus of $C$. The distribution…
The motion of a bead on a rotating circular hoop is investigated using elementary calculus and simple symmetry arguments. The peculiar trajectories of the bead at different speeds of rotation of the hoop are presented. Phase portraits and…
We present a second order accurate in time numerical scheme for curve shortening flow in the plane that is unconditionally monotone. It is a variant of threshold dynamics, a class of algorithms in the spirit of the level set method that…
An analysis is made of a moving disturbance using a directed cyclic graph. A statistical approach is used to calculate the alternative positions in space and state of the disturbance with a defined observed time. The probability for a…
This paper develops a framework for conceptualizing, visualizing, and measuring regularities in rhythmic data. I propose to think about rhythmic data in terms of interval segments: fixed-length groups of consecutive intervals, which can be…
This paper presents a comprehensive analysis of several aspects of the sinh-Gordon equation within a periodic setting. Our investigation proceeds in three main stages. First we establish the existence of periodic solutions for a fixed wave…
Existing algorithms for fitting the parameters of a sinusoid to noisy discrete time observations are not always successful due to initial value sensitivity and other issues. This paper demonstrates the techniques of FIR filtering, Fast…
Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting an array in up to K segments. We want segments to be as monotonic as possible and to alternate signs. We propose a quality metric for…
An emerging way to deal with high-dimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work…
We study polygonal analogues of several moving boundary problems and their time discretization which preserves the constant area speed property. We establish various polygonal analogues of geometric formulas for moving boundaries and make…
Squared deviations from the equilibrium positions of one-dimensional coupled harmonic oscillators with fixed and free endpoints are calculated, and the time averages are expressed as a function of the initial displacements and velocities.…
A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force and Magnus force are taken into account with the use of the quadratic laws. We consider the asymptotic motion of the…
Motions with respect to one inertial (or ``map'') frame are often described in terms of the coordinate time/velocity pair (or ``kinematic'') of the map frame itself. Since not all observers experience time in the same way, other…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
A new algorithm for estimating the time-varying frequency of a noiseless sinusoidal signal is considered. It is assumed that the amplitude and frequency of the sinusoidal signal are unknown functions of time, but are solutions of linear…