Mathematical Principles of Mechanics and Electromagnetism
Part A: Analytical and Continuum Mechanics
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Chapter
Subfluids
This lecture concerns a class of simple materials 1 called simple subfluids, or more briefly subfluids. These are simple materials for which the isotropy group contains a dilatation group, i.e., a group of all un...
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Book
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Chapter
General Relativistic Theory of Electromagnetism
In the general theory of relativity the event world is represented by the Minkowskian manifold C whose structure is determined by the distribution of the stress-energy-momentum tensors on C in accord with Einstei...
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Chapter
Hamiltonian Systems in Phase Space
The equations of Lagrange, which we have derived in Chapter 1, may be transformed into a system of first-order differential equations when the generalized force possesses a potential function. The transformati...
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Chapter
Some Topics in the Statics and Dynamics of Material Bodies
There is a vast literature in continuum mechanics on topics ranging from the classical theories of hydrodynamics and linear elasticity to the modern theories of materials with memory effects and dislocations. ...
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Chapter
Classical Theory of Electromagnetism
The classical theory of electromagnetism is formulated on the basis of a particular frame of reference, called the rest frame or the ether frame, in the Newtonian space-time. We develop this theory in four stages...
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Chapter
General Relativistic Theory of Gravitation
The special theory of relativity summarized in the preceding chapter was formulated by Einstein in order to resolve the difficulties in the classical theory of electromagnetism with regard to a change of inert...
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Chapter
Lagrangian Mechanics of Particles and Rigid Bodies
In classical mechanics the subject analytical dynamics is concerned with motions of particles and rigid bodies. These physical entities may be represented by mathematical models possessing only a finite number of...
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Chapter
Basic Principles of Continuum Mechanics
Continuum mechanics is the branch of classical mechanics concerned with motions of deformable material bodies. The mathematical model for such a body is called a body manifold which is an oriented 3-dimensional d...
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Chapter
Special Relativistic Theory of Electromagnetism
One of the difficulties in the classical theory of electromagnetism is the condition that the Maxwell-Lorentz ether relations D = E, B = H for a vacuum are not invariant under a general Galilean transformation. A...
