主转动角与主转动轴的显式表示

The Explicit Representation to the Principal Rotation Angle and the Principal Rotation Axis

Department of Applied Mechanics, Nanjing University of Science and Technology, Nanjing 210094, P R China

摘要: 本文利用Cayley-Hamilton定理,给出了两种直接获得转动张量显式表示的方法。一种为只含变形梯度较低次幂的表达形式,利用此表示,获得了主转动角的计算公式和主转动轴的显式表示。而另一种则是不含复杂系数且含变量个数较少的高效获得转动张量的方法。进一步,给出了主转动角和主转动轴的一些性质。
- 转动张量 /
- 主转动角 /
- 主转动轴
Abstract: By using Cayley-Hamilton theorem, two kinds of explicit representation for the rotation tensor are proposed. The one contains the lower powers of deformation gradient, by which the formula of the principal rotation angle and the explicit representation of principal axis are obtained;the other, a high efficient method to obtain the rotation tensor, does not contain the complicated coefficients and uses few variables. Some properties about the principal rotation angle and principal rotations axis are obtained.
- stretch tensor /
- principal rotation angle /
- principal rotation axis

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