Results 251 to 260 of about 1,007,209 (285)

Limit Sets of Trajectories

1991
Dynamical polysystems defined on closed manifolds and consisting of finite number of smooth vector fields are considered. ω-limit sets of their trajectories are studied. If a polysystem consists of one vector field we have an old and difficult problem in the Qualitative Theory of differential equations.
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Homoclinic trajectories of invariant sets of Hamiltonian systems

NoDEA : Nonlinear Differential Equations and Applications, 1997
This paper considers positive definite time-periodic Hamiltonian systems. The author reviews the conditions on equilibria (i.e., local maxima of the potential energy) which guarantee the existence of homoclinic trajectories. He then uses variational methods to establish that similar conditions on Mather sets also guarantee the existence of homoclinic ...
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Localizing Sets and Behavior of Trajectories of Time-Varying Systems

Differential Equations, 2019
In this paper, the author dealt with the localization problem, that is, the problem of constructing domains in the system state-space that contain all invariant compact sets for the system of a time-varying ordinary differential equations \[ \dot x=f(t,x),\ f\in C^1\left(\mathbb{R}\times\mathbb{R}^n;\mathbb{R}^n\right), \] and described the typical ...
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ON LIMIT SETS OF TRAJECTORIES OF DYNAMICAL SYSTEMS OF GRADIENT TYPE

Mathematics of the USSR-Sbornik, 1983
Translation from Mat. Sb., Nov. Ser. 116(158), 502-514 (Russian) (1981; Zbl 0498.34020).
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Spacecraft Trajectory Optimization Based on Discrete Sets of Pseudo-Impulses

AIAA/AAS Astrodynamics Specialist Conference and Exhibit, 2008
A brief review of new methods for continuous-thrust trajectory optimization is presented. The methods use discretization of the spacecraft trajectory on segments and sets of pseudoimpulses for each segment. Boundary conditions are presented as a linear matrix equation.
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Stability of a set of trajectories of nonlinear dynamics

Doklady Mathematics, 2007
The stability problem and the stability conditions for the set of stationary solutions for the system of a set of differential equations \[ D_HX=F(t,X), \quad X(t_0)=X_0\in K_c(\mathbb R^n) \] is stated in terms of the existence of a suitable matrix-valued function, where \(t_0\geq 0\), \(F\in C(\mathbb R_+ \times K_c(\mathbb R^n),K_c(\mathbb R^n))\), \
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Enumeration of complete set of flock patterns in trajectories

Proceedings of the 5th ACM SIGSPATIAL International Workshop on GeoStreaming, 2014
In this paper, we consider the problem of mining the complete set of spatio-temporal patterns, called maximal-duration flock patterns (Gudmundsson and van Kreveld, Proc. ACM GIS 2006) from massive mobile GPS location streams. Such algorithms are useful for mining and analysis of real-time geographic streams in geographic information systems. Although a
Xiaoliang Geng, Takuya Takagi, Hiroki Arimura, Takeaki Uno   +3 more
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Study of Genetic Algorithm Settings for Trajectory Optimisation

54th International Astronautical Congress of the International Astronautical Federation, the International Academy of Astronautics, and the International Institute of Space Law, 2003
Genetic algorithms have been used for over 20 years in various applications of optimisation. Also, in optimisation of space applications these algorithms have been studied and occasionally used. Applications of genetic algorithms in the European Space Agency (ESA) date back to 1985.
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Analysis of the Set of Trajectories of Fuzzy Equations of Perturbed Motion

Ukrainian Mathematical Journal, 2015
In this paper, the authors consider a fuzzy model of equations of a perturbed motion of a system with inexact values of the parameters, i.e., \[ \frac{dx}{dt}=f(t,x,\alpha),\,\, x(t_0)=x_0, \] where \(x\in E^n,\) \(f\in C(\mathbb{R}_+\times E^n\times J,E^n),\) \(\alpha\in J\) is a fuzziness parameter, and \(J\) is a compact set in \(\mathbb{R}^d\).
Martynyuk, A. A., Martynyuk-Chernienko, Yu. A.   +1 more
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Dissimilarities Between Trajectories of a Three-Way Longitudinal Data Set

1998
This paper deals with the problem of evaluating dissimilarities between trajectories in a three-way longitudinal data set (a set of multiple time series). The dissimilarity between trajectories is defined as a conic combination of the dissimilarities between trends, velocities and accelerations of the pair of trajectories.
D'URSO, Pierpaolo, VICHI, Maurizio
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