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A foundation is laid for future analyses of gravitation theories. This foundation is applicable to any theory formulated in terms of geometric objects defined on a 4-dimensional spacetime manifold. The foundation consists of (i) a glossary of fundamental concepts; (ii) a theorem that delineates the overlap between Lagrangian-based theories and metric theories; (iii) a conjecture (due to Schiff) that the weak equivalence principle implies the Einstein equivalence principle; and (iv) a plausibility argument supporting this conjecture for the special case of relativistic, Lagrangian-based theories.

Within the past few months two excellent summaries of the state of our knowledge of the weak interactions have been presented.(1,2) Correspondingly, we will not attempt a comprehensive review but instead concentrate this discussion on the status of CP violation; the question of the neutral currents, and the weak equivalence principle.

We construct a Lorentz-covariant theory of gravitation with linear field equations which accounts for all the observational facts,i.e., the three tests of general relativity, with only one adjustable parameter apart from the gravitational coupling constant. The equations of motion of the theory arise both from a variational principle and from the conservation law of the total energy-momentum tensor of the system. The conservation law of mass is also satisfied.

The WEP is proven to hold in a scalar-vector gravitation model with spatially variable speed of light and Lorentz-Poincar\'e type interpretation for the configuration of a non-stationary source \cite{Broekaert2006}. In this model the spatially-VSL, $\mathbf{c}(r) = \mathbf{c'} \Phi^2 + \mathbf{w}$, is a coordinate velocity in contrast to the invariant velocity $c'$, which is locally observable due to the application of the gravitationally modified Lorentz Transformations for space and time intervals \cite{Broekaert2005b}. The Hamiltonian mechanics for particles and photons derived from the corresponding energy and momentum transformations agrees at least till 1-PN with the dynamics of General Relativity Theory \cite{Broekaert2004b}. Now in a local inertial frame and for a non-stationary source the validity of the WEP is proven by deriving the nil relative acceleration of a locally coincident free-falling particle. This is established by adapting the derivative to incorporate the conventionalprocedure of localizing its arguments by means of \emph{parallel transport}. This transport over a free-fall trajectory can be naturally expressed using a composition of gravitationally modified Lorentz transformations.

This paper aims to present a precise proof of the nontrivial fact that a virtual work principle is also valid for two different physical systems, a parallel manipulator and its arbitrary reduced tree system, through introducing the so called inertia equivalence principle that exposes the relation between the dynamics of the two systems. Dynamics of parallel manipulators and its properties are then derived based on geometric projection. The role of redundant action in removing singularities is also clarified. Two control algorithms are studied. First, we implement a geometric control algorithm that is based on the Riemannian metric structure. Motivated by this, an adaptive control algorithm is then proposed in which only the dynamic parameters need to be updated. Geometric reinterpretation of this algorithm as the passive system is given. Its asymptotic stability is therefore an obvious fact. The new content of this algorithm compared with the traditional ones is discussed. Experimental results are then reported.

For a given space-time and for an arbitrary time-like geodes ic, we analyze the conditions for the construction of Fermi coordinates so that they are also rigi d covariant. We then apply these conditions to linear plane gravitational waves

An equivalence principle for mechanical and magnetoelastic stresses is used for the quantitative theoretical description of giant magnetostrain effect in ferromagnetic martensite. Field-induced strains are computed in the framework of phenomenological magnetoelastic model for two different orientations of magnetic field with respect to the crystal axes. Good agreement between the theoretical and experimental field dependencies of the strains in Ni–Mn–Ga alloys is achieved.

All metric theories of gravity (including general relativity) are based on the Einstein equivalence principle (EEP), which states in part that the outcome of any local nongravitational experiment is independent of the velocity and orientation of the freely falling laboratory apparatus. This part of the EEP is called local Lorentz invariance (LLI).

The purpose of this note is to prove, under the hypothesis of validity of:a) the Heisenberg indefiniteness principle,b) Lorentz transformation in a local inertial frame,c) the « equivalence principle », the existence of a minorant of the indefiniteness for the measurement of a position. « Planck radius » appears to be such a minorant.

The main stages in the construction of the theory of gravitation and prospects for its further development are discussed. The main attention is devoted to comparing the properties of the relativistic gravitational field and other physical fields. Two equivalent formulations of the general theory of relativity—the geometrical and the field— are considered in detail. It is explained why some of the field theories of gravitation developed in flat space-time are not different theories of the relativistic gravitational field but merely other formulations of general relativity.

Present-day theory of uniform cylindrical dielectric-rod antennas rests on the three theoretical treatments of Horton, Bouix and Fradin (leaky-guide theory), and on Brown's end-fire theory. A digression on the general relationship between Schelkunoff's equivalence principle and the vector Kirchhoff formula reveals that these radiation formulas may only be applied to regions in which the vector potentials are known to satisfy the inhomogeneous wave equation. On applying this axiom to the theories, all but Brown's are shown to be fallacious. A detailed application of the vector Kirchhoff formula to uniform cylindrical dielectric rods supporting the HE11 mode produces an expression for the far-field radiation pattern, which, when computed, gives good agreement with existing experimental data. The analysis allows for dielectric losses and can also be extended to nonuniform dielectric antennas with gradual tapers. Fresnel interaction of the apertures and lens effects are considered. Finally, some design recommendations for dielectric rod antennas are made.

We may take the view that either the many scalar-tensor formalisms (of Jordan, Brans and Dicke, Hoyle, etc.) are all new and distinctly different theories of gravitation, or they are implicit within the theory of general relativity and therefore do not qualify as new theories of gravitation. There are cogent and persuasive reasons for adopting the latter view.