# A. D. Alexandrovs length manifolds with one-sided bounded by Berestovskii V. N.

By Berestovskii V. N.

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27) lead to the formulation with material reference and material parametrization. 29) and pushed forward to the spatial configuration. 24). The four different versions of the volume specific balance of momentum of the material motion problem are summarized in the following. 32) dt Pt = div π td + Bt To illustrate the duality with the spatial motion problem, we can formally introduce the following Neumann type boundary conditions relating the momentum fluxes π td and Σ td to the sum of the closed and the open system material stress vector contributions open T τclosed and T τ .

Coussy [35], Ulm & Coussy [211], Stark & Wicht [195], Kuhl, Bangert & Meschke [124] or Kuhl & Steinmann [134]. g. in the context of calcium leaching, is a classical example of a mass flux, as illustrated by Ulm et al. [212], Torrenti et al. [208] or Carmeliet [23]. For chemical reactions in general, we refer to the standard textbook by Atkins [10] while the early works of Kirkwood & Oppenheim [120], Katchalsky & Curran [116] and Guggenheim [81] provide excellent introductions to chemical thermodynamics.

The mechanical open forces fclosed , and a reduced open system forces term f¯ , the so–called propulsive force. However, of course, the standard balance equations hold for the overall closed system composed of the rocket head and the exhausted mass. g. 6. open From the above equations, the reduced open system force term f¯ , which is responsible for the rocket thrust, can be identified as the force caused by the difference of the velocity of the ejection v¯ with respect to the rocket head velocity v.