Symplectic Rotational Geometry in Human Biomechanics

Ivancevic, Vladimir G.

doi:10.1137/s003614450341313x

Cited by 25 publications

(74 citation statements)

References 18 publications

(62 reference statements)

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“…The tangent dynamics equation (48) can be used to define Lyapunov exponents in dynamical systems given by the Riemannian action (44) and Hamiltonian (45), using the formula [14]…”

Section: Chaotic Inter-phase In Crowd Dynamics Induced By Its Riemannmentioning

confidence: 99%

Entropic Geometry of Crowd Dynamics

Ivancevic¹,

Reid²

2010

Nonlinear Dynamics

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“…The tangent dynamics equation (48) can be used to define Lyapunov exponents in dynamical systems given by the Riemannian action (44) and Hamiltonian (45), using the formula [14]…”

Section: Chaotic Inter-phase In Crowd Dynamics Induced By Its Riemannmentioning

confidence: 99%

Entropic Geometry of Crowd Dynamics

Ivancevic¹,

Reid²

2010

Nonlinear Dynamics

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“…This kinematically validated human motion simulator has been described in a series of papers and books [Ivancevic and Snoswell 2001, Ivancevic and Beagley 2003, Ivancevic 2002, Ivancevic 2004, Ivancevic and Beagley 2005, [Ivancevic and Ivancevic 2006a, Ivancevic and Ivancevic 2006b, Ivancevic and Ivancevic 2006c, [Ivancevic and Ivancevic 2007d, Ivancevic and Ivancevic 2007e, Ivancevic 2006, Ivancevic and Ivancevic 2007a, Ivancevic and Ivancevic 2007b.…”

Section: Coupled-loading-rate Hypothesismentioning

confidence: 99%

New Mechanics of Generic Musculo-Skeletal Injury

Ivancevic

2009

Biophys. Rev. Lett.

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Prediction and prevention of musculo-skeletal injuries is an important aspect of preventive health science. Using as an example a human knee joint, this paper proposes a new coupledloading-rate hypothesis, which states that a generic cause of any musculo-skeletal injury is a Euclidean jolt, or SE(3)−jolt, an impulsive loading that hits a joint in several coupled degreesof-freedom simultaneously. Informally, it is a rate-of-change of joint acceleration in all 6-degreesof-freedom simultaneously, times the corresponding portion of the body mass. In the case of a human knee, this happens when most of the body mass is on one leg with a semi-flexed kneeand then, caused by some external shock, the knee suddenly 'jerks'; this can happen in running, skiing, sports games (e.g., soccer, rugby) and various crashes/impacts. To show this formally, based on the previously defined covariant force law and its application to traumatic brain injury [Ivancevic 2008], we formulate the coupled Newton-Euler dynamics of human joint motions and derive from it the corresponding coupled SE(3)−jolt dynamics of the joint in case. The SE(3)−jolt is the main cause of two forms of discontinuous joint injury: (i) mild rotational disclinations and (ii) severe translational dislocations. Both the joint disclinations and dislocations, as caused by the SE(3)−jolt, are described using the Cosserat multipolar viscoelastic continuum joint model.

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“…In order to formalize the Lewinian life-space concept, a set of action principles need to be associated to Lewinian force-fields, (loco)motion paths (rep-resenting mental abstractions of biomechanical paths [17]) and life space geometry. As an extension of the Lewinian concept, in this paper we introduce a new concept of life-space foam (LSF, see Figure 1).…”

Section: Lewinian Life Spacementioning

confidence: 99%

Life-space foam: A medium for motivational and cognitive dynamics

Ivancevic

Aidman

2007

Physica A: Statistical Mechanics and its Applications

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General stochastic dynamics, developed in a framework of Feynman path integrals, have been applied to Lewinian field-theoretic psychodynamics [1,2,13], resulting in the development of a new concept of life-space foam (LSF) as a natural medium for motivational and cognitive psychodynamics. According to LSF formalisms, the classic Lewinian life space can be macroscopically represented as a smooth manifold with steady force-fields and behavioral paths, while at the microscopic level it is more realistically represented as a collection of wildly fluctuating force-fields, (loco)motion paths and local geometries (and topologies with holes). A set of leastaction principles is used to model the smoothness of global, macro-level LSF paths, fields and geometry. To model the corresponding local, micro-level LSF structures, an adaptive path integral is used, defining a multi-phase and multi-path (multifield and multi-geometry) transition process from intention to goal-driven action. Application examples of this new approach include (but are not limited to) information processing, motivational fatigue, learning, memory and decision-making.

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Symplectic Rotational Geometry in Human Biomechanics

Cited by 25 publications

References 18 publications

Entropic Geometry of Crowd Dynamics

Entropic Geometry of Crowd Dynamics

New Mechanics of Generic Musculo-Skeletal Injury

Life-space foam: A medium for motivational and cognitive dynamics

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