Tensors of Rank Two in Tensor Flight Dynamics

• 作者: Peter H. Zipfel
• 来源期刊: 航空科学与技术(英文)
• 学科: 数学
• 关键词: TENSOR Flight DYNAMICS COVARIANCE Principle EINSTEIN Rotation TENSOR Angular Velocity TENSOR Moment of INERTIA TENSOR Rotational Time Derivative Euler Transformation INS Missile DYNAMICS
• 年，卷（期）: 2018,（2）
• 页码范围: 11-19
• 页数: 9页
• 分类号: O1

摘要

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.