Sentence examples for transformation law from inspiring English sources

Without insisting on a pictorial image, a tensor is defined as an objective entity having components that change according to a transformation law that is a generalization of the vectorial transformation law but that retains the two key properties of that law.

Transformation law for acceleration: The transformation law for acceleration is linear, but is not homogeneous in the acceleration variable.

The transformation law for the 3-acceleration is much more complicated than that of the 4-acceleration.

Hence the coefficients \ \Gamma^{i}_{jk}(x)\) do not constitute a tensor; they conform to a linear but non-homogeneous transformation law.

Since the transformation law of the projective structure \ \Pi^{\alpha}_{2}(x^{i}, \xi^{\alpha}_{1}\)) has the same inhomogeneous form as the 3-acceleration \(\xi^{\alpha}_{2}\), the difference also transforms linearly and homogeneously.

The inhomogeneity of the transformation law of the 3-acceleration entails that an acceleration that is zero with respect to one coordinate system is not zero with respect to another coordinate system.

The corresponding compensator can be directly calculated and thus efficiently implemented from the model by analytical transformation laws.

From a physics standpoint, this amounts to arranging fields in multiplets with respect to the conformal group but with novel Weyl transformation laws.

As an example consider the transformation laws for the 4-velocity and the 4-acceleration.

In such a situation, tangent vectors, or more generally, tensors at two different points \(x^{i}\) and \(x^{i} + dx^{i}\), obey different transformation laws; consequently, their difference is not a tensor.

This shows that while the differential topological structure of spacetime gives us sufficient structure to do calculus and to derive the transformation laws for 4-velocities and 4-accelerations by way of simple differentiation, it does not provide sufficient structure with which to determine a standard of zero 4-acceleration.