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Vectors
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... But b and c have no common factor because we are assuming that (a, b, c) is a Lorentzian primitive Pyhtagorean triple. So d must equal to 1 or 2. But d also divides (b − c) (b + c) = a2 , and a is odd, so d must be 1. In other words, the only number dividing both b − c and b + c is 1, so b − c and b ...
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... (g) Find the angle between two lines and the point of intersection of two lines when it exists. Differential Equations (a) Formulate a simple statement involving a rate of change as a differential equation, introducing, if necessary, a constant of proportionality; (b) Find by integration a general f ...
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Time History Forced Response in Nonlinear Mechanical Systems

... Abstract. A formulation of a digital filter method for computing the forced response of a linear MDOF mechanical system is proposed. It is shown how aliasing error effects can be avoided at the expense of a bias error. The bias error is however completely known and it is system independent, as it on ...
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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.
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