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https://doi.org/10.1016/0039-3681(78)90008-0

has been cited by the following article:

• TITLE: Covariant Newtonian Dynamics and the Principle of Material Frame-Indifference

  AUTHORS: Peter H. Zipfel

  KEYWORDS: Einstein, Galileo Galilei, Newton’s Second Law, Tensor Flight Dynamics, Computer Programming

  JOURNAL NAME: Advances in Aerospace Science and Technology, Vol.9 No.4, November 6, 2024

  ABSTRACT: As all natural laws, Newtonian dynamics should be governed by Einstein’s Covariance Principle; i.e., being covariant under all coordinate transformations, even time-dependent transformations. But Newton’s Second Law, as it is generally understood, is unchanged only under Galilean transformations, which do not include time-dependent coordinate transformations. To achieve the covariant formulation of Newton’s Second Law, a distinction must be made between frames and coordinate systems, as advanced by the Principle of Material Frame-Indifference, and furthermore, the ordinary time derivative must be replaced by the rotational time derivative. Elevating Newton’s Second Law to covariancy has born many fruits in flight dynamics from the theoretical underpinning of unsteady flight maneuvers to the practical modeling of complex flight engagements in tensors, followed by efficient programming with matrices.