scholarly journals Jet methods in time-dependent Lagrangian biomechanics

Open Physics ◽  
2010 ◽  
Vol 8 (5) ◽  
Author(s):  
Tijana Ivancevic
Keyword(s):  
Human Body ◽  
Degrees Of Freedom ◽  
Vector Fields ◽  
Differential Forms ◽  
Flow Equation ◽  
Body Motion ◽  
Time Dependent ◽  
Metric Tensor ◽  
Geometric Evolution ◽  
Configuration Manifold

AbstractIn this paper 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 associated to the extended musculo-skeletal configuration manifold, called the configuration bundle. We start with an ordinary configuration manifold of human body motion, given as a set of its all active degrees of freedom (DOF) for a particular movement. This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. By this extension, using techniques from fibre bundles, we defined the biomechanical configuration bundle. On the biomechanical bundle we define vector-fields, differential forms and affine connections, as well as the associated jet manifolds. Using the formalism of jet manifolds of velocities and accelerations, we develop the time-dependent Lagrangian biomechanics. Its underlying geometric evolution is given by the Ricci flow equation.

Differential geometry

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Differential Geometry ◽  
Vector Fields ◽  
Differential Forms ◽  
Curvilinear Coordinates ◽  
Moving Frames ◽  
Tensor Fields ◽  
Metric Tensor ◽  
Vector Calculus ◽  
Vector Version ◽  
Definition Of

This chapter presents some elements of differential geometry, the ‘vector’ version of Euclidean geometry in curvilinear coordinates. In doing so, it provides an intrinsic definition of the covariant derivative and establishes a relation between the moving frames attached to a trajectory introduced in Chapter 2 and the moving frames of Cartan associated with curvilinear coordinates. It illustrates a differential framework based on formulas drawn from Chapter 2, before discussing cotangent spaces and differential forms. The chapter then turns to the metric tensor, triads, and frame fields as well as vector fields, form fields, and tensor fields. Finally, it performs some vector calculus.

Geometric description of time-dependent finite-dimensional mechanical systems

2020 ◽  
Vol 25 (11) ◽  
pp. 2050-2075
Author(s):  
Simon R. Eugster ◽  
Giuseppe Capobianco ◽  
Tom Winandy
Keyword(s):  
State Space ◽  
Degrees Of Freedom ◽  
Vector Fields ◽  
Mechanical Systems ◽  
Second Order ◽  
The State ◽  
Time Dependent ◽  
Finite Dimensional ◽  
Affine Bundle ◽  
Time Position

Using the non-standard geometric structure proposed by Loos, we present a coordinate-free formulation of the theory for time-dependent finite-dimensional mechanical systems with n degrees of freedom. The state space containing the system’s information on time, position and velocity is defined as a (2 n+1)-dimensional affine bundle over an ( n+1)-dimensional generalized space-time. The main goal is to present a geometric postulate that characterizes a second-order vector field whose integral curves describe the motions of a time-dependent finite-dimensional mechanical system. The core objects of the postulate are differential two-forms on the state space, called action forms, which are in a bijective relation with second-order vector fields. The requirements for a differential two-form to be an action form allow for a coordinate-free definition of non-potential forces, which may depend on time, position and velocity. Finally, we show that not only Lagrange’s equations but also Hamilton’s equations follow directly as mere coordinate representations of the same coordinate-free postulate.

Learning Coordination in Body Motion Control: A Pattern Based Approach

2017 ◽  
Author(s):  
Shuichi Fukuda
Keyword(s):  
System Dynamics ◽  
Motion Control ◽  
Human Body ◽  
Degrees Of Freedom ◽  
Explicit Knowledge ◽  
Large Data ◽  
Body Motion ◽  
Unit Space ◽  
The Difference ◽  
The Ideal

Motion Control is increasing its importance. Although the progress of system dynamics is remarkable, progress of human body motion control is very slow. Most of system dynamics deal with explicit knowledge, but human body motion control belongs to tacit knowledge. Its difficulty is the number of degrees of freedom is tremendously large and human behaviors change very flexibly to cope with the changing contexts of environments and situations. Further, our body motions vary from person to person, because our bodies, muscles and joints are different. These problems make it very difficult to deal with human body motions. Although there are many researches using motion capture, EMG, etc., they succeeded only in showing how final successful movements should be. They can show movements at each step toward this goal, but they cannot teach learners how they should coordinate their muscles or joints. Coordination or balancing plays an important role in body motion learning, But, there are very few, in any, researches which help learners learn how to coordinate or balance their muscles and joints to achieve the final successful movement. In this paper, a solution to how we can help a learner learn to coordinate or balance in motion or motor learning is introduced. Its approach is pattern based and it uses Recognition Taguchi (RT) technique, one of the techniques of Mahalanobis Taguchi Systems. In this approach, Mahalanobis Distance (MD) is used to indicate quantitatively how a learner’s pattern of movement is close to the successful one. MD reduces multi-dimensional information to one-dimensional. RT indicates how a sample pattern matches the ideal pattern quantitatively using MD. In the regular RT approach, Unit Space (Ideal Pattern) is defined and each sample space is compared with Unit Space using MD. But In this work, Unit Space is updated every time a learner succeeds, such as successfully riding a bicycle. And every trial movement is compared with this updated Unit Space. The primary benefits of RT are it can process large data in a very short time and it is based upon the difference between the ideal pattern and the current pattern. So, learners can understand which joints they should pay attention to in order to coordinate or balance to improve their movements. Thus, step by step, they can coordinate or balance their muscles and joints to get closer to the ideal movement.

Introduction

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Degrees Of Freedom ◽  
State Level ◽  
Boltzmann Distribution ◽  
Theoretical Description ◽  
Time Dependent ◽  
Nuclear Dynamics ◽  
Molecular Reaction ◽  
Oppenheimer Approximation

This introductory chapter considers first the relation between molecular reaction dynamics and the major branches of physical chemistry. The concept of elementary chemical reactions at the quantized state-to-state level is discussed. The theoretical description of these reactions based on the time-dependent Schrödinger equation and the Born–Oppenheimer approximation is introduced and the resulting time-dependent Schrödinger equation describing the nuclear dynamics is discussed. The chapter concludes with a brief discussion of matter at thermal equilibrium, focusing at the Boltzmann distribution. Thus, the Boltzmann distribution for vibrational, rotational, and translational degrees of freedom is discussed and illustrated.

scholarly journals Task space adaptation via the learning of gait controllers of magnetic soft millirobots

2021 ◽  
pp. 027836492110218
Author(s):  
Sinan O. Demir ◽  
Utku Culha ◽  
Alp C. Karacakol ◽  
Abdon Pena-Francesch ◽  
Sebastian Trimpe ◽  
...  
Keyword(s):  
Human Body ◽  
Degrees Of Freedom ◽  
Bayesian Optimization ◽  
Small Scale ◽  
Soft Robots ◽  
Modeling And Control ◽  
Walking Gait ◽  
Physical Experiments ◽  
Efficient Learning ◽  
Task Environments

Untethered small-scale soft robots have promising applications in minimally invasive surgery, targeted drug delivery, and bioengineering applications as they can directly and non-invasively access confined and hard-to-reach spaces in the human body. For such potential biomedical applications, the adaptivity of the robot control is essential to ensure the continuity of the operations, as task environment conditions show dynamic variations that can alter the robot’s motion and task performance. The applicability of the conventional modeling and control methods is further limited for soft robots at the small-scale owing to their kinematics with virtually infinite degrees of freedom, inherent stochastic variability during fabrication, and changing dynamics during real-world interactions. To address the controller adaptation challenge to dynamically changing task environments, we propose using a probabilistic learning approach for a millimeter-scale magnetic walking soft robot using Bayesian optimization (BO) and Gaussian processes (GPs). Our approach provides a data-efficient learning scheme by finding the gait controller parameters while optimizing the stride length of the walking soft millirobot using a small number of physical experiments. To demonstrate the controller adaptation, we test the walking gait of the robot in task environments with different surface adhesion and roughness, and medium viscosity, which aims to represent the possible conditions for future robotic tasks inside the human body. We further utilize the transfer of the learned GP parameters among different task spaces and robots and compare their efficacy on the improvement of data-efficient controller learning.

Ride Comfort Evaluation of Horizontal Vibration in Tractor-Trailer Considering Human Body Motion of Driver

2013 ◽  
Author(s):  
Yuichiro Hirose ◽  
Mitsuru Enomoto ◽  
Takashi Sasaki ◽  
Eiichi Yasuda ◽  
Masatoshi Hada
Keyword(s):  
Human Body ◽  
Ride Comfort ◽  
Body Motion ◽  
Horizontal Vibration ◽  
Comfort Evaluation ◽  
Ride Comfort Evaluation

A Two-Dimensional Linear Assumed Strain Triangular Element for Finite Deformation Analysis

2005 ◽  
Vol 73 (6) ◽  
pp. 970-976 ◽  
Author(s):  
Fernando G. Flores
Keyword(s):  
Finite Deformation ◽  
Degrees Of Freedom ◽  
Yield Function ◽  
Triangular Element ◽  
Deformation Analysis ◽  
Elastic Model ◽  
Stress Strain ◽  
Metric Tensor ◽  
Assumed Strain ◽  
Non Linear

An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then nonconforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. A hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong nonlinearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.

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