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Inspired by amazing result obtained by Semay (2018), this study revisits generalised Kepler’s third law of an n-body system from the perspective of dimensional analysis. To be compatible with Semay’s quantum n-body result, this letter reports a conjecture which had not be included in author’s early publication (Sun, 2018) but formulated in the author’s research memo. The new conjecture for quantum N-body system is proposed as follows: Tq|Eq|3/2=π2G∑i=1N∑j=i+1Nmimj3∑k=1Nmk1/2. This formulae is, of course, consistent with the Kepler’s third law of 2-body system, and exact same as Semay’s quantum result for identical bodies. Keywords: Kepler’s third law, N-body system, Periodic orbits, Dimensional analysis, Classical and quantum mechanics

This article attempts to clarify an issue regarding the proper definition of plastic dislocation density tensor. This study shows that the Ortiz’s and Berdichevsky’s plastic dislocation density tensors are equivalent with each other, but not with Kondo’s one. To fix the problem, we propose a modified version of Kondo’s plastic dislocation density tensor. Keywords: Elasto-plasticity, Deformation gradient, Plastic dislocation density tensor

This article is mainly focussed on revisited of the two well-known postulates of plasticity, i.e., the Drucker and the Il’iushin postulate, and it describes their rational interpretation within the framework of irreversible thermodynamics and using exterior calculus. It shows that the Il’iushin and the Drucker postulate is the integral form and local form of the irreversible thermodynamics of plastic deformation, respectively. The Drucker and Il’iushin postulate is equivalent for both soft and hardening materials.