KINETIC EQUATION FOR SOLITONS illjl = -4 (.!._)` ljJ -~( u
... of the phase shifts in paired collisions. We note, however, that the solutions of the systems {11) and (12), which represent the limiting states of the soliton as t - ± oo, depend only on the amplitudes of the remaining solitons and do not depend on their positions, which are determined by their pha ...
... of the phase shifts in paired collisions. We note, however, that the solutions of the systems {11) and (12), which represent the limiting states of the soliton as t - ± oo, depend only on the amplitudes of the remaining solitons and do not depend on their positions, which are determined by their pha ...
Vector Math.indd
... Time. 3:00 PM, 6 minutes (m), 11 hours (h), 1 decade, etc., are examples of time. The magnitude or size of time is a real number. There are units (minutes, hours, etc.). However, there is no direction. Hours do not move up, minutes do not go east, 3:00 PM does not point to the left. Time is a scalar ...
... Time. 3:00 PM, 6 minutes (m), 11 hours (h), 1 decade, etc., are examples of time. The magnitude or size of time is a real number. There are units (minutes, hours, etc.). However, there is no direction. Hours do not move up, minutes do not go east, 3:00 PM does not point to the left. Time is a scalar ...
The jerk vector in projectile motion
... The initial conditions at time t = 0 are given by v x v0 cos ; v y v0 sin ; x = 0; y = 0. Eqs. (1) and (2) are uncoupled equations which can be integrated separately. Integrating them twice with respect to t and applying the initial conditions, we obtain ...
... The initial conditions at time t = 0 are given by v x v0 cos ; v y v0 sin ; x = 0; y = 0. Eqs. (1) and (2) are uncoupled equations which can be integrated separately. Integrating them twice with respect to t and applying the initial conditions, we obtain ...
systems of particles
... Vector Mechanics for Engineers: Dynamics Introduction • In the current chapter, you will study the motion of systems of particles. • The effective force of a particle is defined as the product of it mass and acceleration. It will be shown that the system of external forces acting on a system of part ...
... Vector Mechanics for Engineers: Dynamics Introduction • In the current chapter, you will study the motion of systems of particles. • The effective force of a particle is defined as the product of it mass and acceleration. It will be shown that the system of external forces acting on a system of part ...
Section one: Sensitive Dependence on Initial Conditions
... One Dimensional Chaos In this chapter , we study many methods of describing the way in which iterates of neighboring points separate from another : sensitive dependence on initial conditions , Lyapunov exponent and the transitivity. These notions are fundamental to the concept of chaos, which also w ...
... One Dimensional Chaos In this chapter , we study many methods of describing the way in which iterates of neighboring points separate from another : sensitive dependence on initial conditions , Lyapunov exponent and the transitivity. These notions are fundamental to the concept of chaos, which also w ...
Some properties of the space of fuzzy
... wise bounded on [0, 1]. From the condition (3), we know that {u n ()} and {u n ()} are equi-left-continuous on (0, 1]. Hence, by Theorem 2.2, we infer that {u n } has a d∞ -convergent subsequence {u ni }. By (2), U is a closed subset of E1 and {u ni } ⊂ U . Hence there exists u ∈ U such that d∞ (u ...
... wise bounded on [0, 1]. From the condition (3), we know that {u n ()} and {u n ()} are equi-left-continuous on (0, 1]. Hence, by Theorem 2.2, we infer that {u n } has a d∞ -convergent subsequence {u ni }. By (2), U is a closed subset of E1 and {u ni } ⊂ U . Hence there exists u ∈ U such that d∞ (u ...
Dynamical system
In mathematics, a dynamical system is a set of relationships among two or more measurable quantities, in which a fixed rule describes how the quantities evolve over time in response to their own values. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake.At any given time a dynamical system has a state given by a set of real numbers (a vector) that can be represented by a point in an appropriate state space (a geometrical manifold). The evolution rule of the dynamical system is a function that describes what future states follow from the current state. Often the function is deterministic; in other words, for a given time interval only one future state follows from the current state; however, some systems are stochastic, in that random events also affect the evolution of the state variables.