Vectors
... EXAMPLE 7 An airplane heads due east at 200 mph through a crosswind blowing due north at 30 mph, and the superposition (i.e., sum) of these two velocities is the airplane’s actual velocity vector. What is the airplane’s actual speed and direction? Solution: The heading velocity vector is 200, 0 an ...
... EXAMPLE 7 An airplane heads due east at 200 mph through a crosswind blowing due north at 30 mph, and the superposition (i.e., sum) of these two velocities is the airplane’s actual velocity vector. What is the airplane’s actual speed and direction? Solution: The heading velocity vector is 200, 0 an ...
Chapter 11
... them much easier to deal with in a polar coordinate system. As we learned in our discussion of vectors, the results of a physical problem are independent of our choice of coordinate system. The coordinate system choice is a matter of convenience in the calculation of the problem (in the case of rect ...
... them much easier to deal with in a polar coordinate system. As we learned in our discussion of vectors, the results of a physical problem are independent of our choice of coordinate system. The coordinate system choice is a matter of convenience in the calculation of the problem (in the case of rect ...
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.