Observer-invariance is regarded as a minimum requirement for an appropriate definition of time derivatives. We derive various time derivatives systematically from a spacetime setting, where observer-invariance is a special case of a covariance principle and covered by Ricci-calculus. The analysis is considered for tangential n-tensor fields on moving surfaces and provides formulations which are applicable for numerical computations. For various special cases, e. g., vector fields ($n=1$) and symmetric and trace-less tensor fields ($n=2$) we compare material and convected derivatives and demonstrate the different underlying physics.

中文翻译：

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移动表面上的观察者不变时间导数

观察者不变性被认为是适当定义时间导数的最低要求。我们从时空设置中系统地推导出各种时间导数，其中观察者不变性是协方差原理的一个特例，并被 Ricci 演算涵盖。该分析考虑了移动表面上的切向n张量场，并提供了适用于数值计算的公式。对于各种特殊情况，e。 g., 向量场 ($n=1$) 和对称和无迹张量场 ($n=2$) 我们比较了材料和对流导数，并展示了不同的基础物理。