时变人体生物力学的Jet-Ricci几何
Jet-Ricci Geometry of Time-Dependent Human Biomechanics
摘要：
我们提出了一个“普通的”自主人体生物力学，其中总机械+生化能量不守恒的时间依赖性的推广。我们介绍了一个一般框架，时间依赖性生物力学的射流流形来自扩展的肌肉骨骼配置流形。相应的黎曼几何演化遵循Ricci流扩散。特别是，我们表明，总生物力学能量的指数样衰减（由于生化资源耗尽）是密切相关的Ricci流的生物力学配置流形。关键词：时变生物力学，扩展构形流形，构形丛，射流流形，Ricci流扩散
英文摘要：
We propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds derived from the extended musculo-skeletal configuration manifold. The corresponding Riemannian geometrical evolution follows the Ricci flow diffusion. In particular, we show that the exponential-like decay of total biomechanical energy (due to exhaustion of biochemical resources) is closely related to the Ricci flow on the biomechanical configuration manifold. Keywords: Time-dependent biomechanics, extended configuration manifold, configuration bundle, jet manifolds, Ricci flow diffusion
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