TITLE:
Tensors of Rank Two in Tensor Flight Dynamics
AUTHORS:
Peter H. Zipfel
KEYWORDS:
Tensor Flight Dynamics, Covariance Principle, Einstein, Rotation Tensor, Angular Velocity Tensor, Moment of Inertia Tensor, Rotational Time Derivative, Euler Transformation, INS, Missile Dynamics
JOURNAL NAME:
Advances in Aerospace Science and Technology,
Vol.3 No.2,
June
22,
2018
ABSTRACT: Tensor flight dynamics solves flight dynamics problems using Cartesian tensors,
which are invariant under coordinate transformations, rather than
Gibbs’ vectors, which change under time-varying transformations. Three tensors
of rank two play a prominent role and are the subject of this paper: moment
of inertia, rotation, and angular velocity tensor. A new theorem is proven
governing the shift of reference frames, which is used to derive the angular
velocity tensor from the rotation tensor. As applications, the general strap-down
INS equations are derived, and the effect of the time-rate-of-change of the
moment of inertia tensor on missile dynamics is investigated.