Drafts by William Luna-Victoria
Provides a derivation of the form of the Lorentz Transformation without assuming speed of light i... more Provides a derivation of the form of the Lorentz Transformation without assuming speed of light is constant. Assumptions used include primarily the principle of relativity, that is that inertial transformation are those that keep the law of physics are invariant, and that inertial transformations sends a trajectories of constant velocity to trajectories of constant velocities. Also include minor assumptions of the existence of trajectories, invariance of length by symmetric transformations, and that positive velocities combine to positive velocities. Form of inertial transformation corresponds to the Lorentz Transformation with a "characteristic speed" c that corresponds to the speed of light in special relativity.
Provides an introduction to the concept and derivation of the Quaternions. Then derives several b... more Provides an introduction to the concept and derivation of the Quaternions. Then derives several basic algebraic relationships involving quaternions, culminating with how quaternions can be used to describe 3d rotations. Then discusses the computational advantages that quaternions have over other 3d rotation methods, and provides an example of a classical mechanics rotation problem being solved with quaternions. Then discusses Frobenius's Theorem and the potential physical implication that it has. Overall aim is to provide a good educational resource for the intuition of quaternions and their applications.
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Drafts by William Luna-Victoria