Download Introduction to Special Relativity by Wolfgang Rindler PDF

By Wolfgang Rindler

ISBN-10: 0198531818

ISBN-13: 9780198531814

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Extra info for Introduction to Special Relativity

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There are many different types of fixed points, defined by their differing stability properties (the one here is called an attractor node because it attracts the field lines to it from all directions). The study of nonlinear dynamical systems pays close attention to the study of fixed points and nullclines. The mathematical details of flows will be covered in Chapter 3, and these principles will be applied in many of the following chapters in this book. 6 Example of a flow diagram in state space showing the vector field and selected stream lines (also called field lines or flow lines).

While the observer in the unprimed frame O experiences no force on himself or herself , the observer in the primed frame ¯ does. This force could be experienced, for instance, as the force of a space-ship O floor on the feet of the observer as it accelerates forward. If the primed observer does not know that the space-ship is the cause of the force, he or she might assume that the force is a gravitational force, and that the same gravitational force was the cause of the observed parabolic trajectory.

5. Therefore, the flow equations define a vector field on the state space. Each point on the state space has exactly one trajectory passing through it, which is drawn as a stream line. 5, only one trajectory (stream line) is drawn. Stream lines are the field lines of the vector field. Much of the study of modern dynamics is the study of the geometric properties of the vector field and field lines associated with a defined set of flow equations. 5 State-space vector field of the damped harmonic oscillator.

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