Forward-dynamics method

Equations (6.1) and (6.7) can be combined to form a model of the musculoskeletal system in which the inputs are the muscle activation histories (a) and the outputs are the body motions (q, 4, q) (Fig. 6.22). Measurements of muscle EMG and body motions can be used to calculate the time histories of the musculotendinous forces during movement (Hof et al., 1987 Buchanan et al., 1993). Alternatively, the goal of the motor task can be modeled and used, together with dynamic optimization theory, to calculate the pattern of muscle activations needed for optimal performance of the task (Hatze, 1976 Pandy et al., 1990 Raasch et al., 1997 Pandy, 2001). Thus, one reason why the forward-dynamics method is potentially more powerful for evaluating musculotendinous forces than... 

If accurate measinements of body motions and external forces are available, then inverse dynamics should be used to determine musculotendinous forces durii movement, because this method is much less expensive computationally. If, instead, the goal is to study how changes in body structure affect function and performance of a motor task, then the forward-dynamics method is preferred, for measurements of body motions and external forces are a priori not available in this instance. 

For the future, it is clear that dynamics methods are almost essential if one is going to examine the interesting results that are coming from femtosecond spectroscopy and to study quantum yields. These methods are just beginning to be exploited, and this is an exciting new direction for quantum chemistry. We have not commented on the role of the solvent or the role of the environment provided by a biochemical system. There are no special problems related to excited state chemistry for the former, and one can look forward to applications to biochemical systems to appear in the near future. 

Estimated rate constants for the various electron-transfer steps, together with approximate reduction potentials, are displayed in Figure 6.39. For each step, the forward rate is orders of magnitude faster than the reverse reaction. The rapid rates suggest that attempts to obtain x-ray structures of intermediates (especially the early ones ) will not be successful. However, molecular dynamics methods are being explored in computer simulations of the structures of various intermediates. Within a few years we may begin to understand why the initial steps are so fast. 

Equations that arise in modeling the dynamics of homogeneous systems are initial value problems, generally approached with techniques of the Euler type. Initial value problems involve derivatives with respect to time these must be discretized, which can be done using the forward Euler method... 

Given the limitations of each method, which should be used forward or inverse dynamics That depends on the question being asked. If one s primary interest is in joint kinematics, it makes more sense to start with a measurement of position as in the invmse dynamics approach. If one is primarily interested in muscle forces, one could argue that forward dynamics has more advantages. For esti-... 

FIGURE 6.22 Comparison of the forward- and inverse-dynamics methods for determining muscle forces during movement. Top Body motions are the inputs and muscle forces are the outputs in inverse dynamics. Thus, measurements of body motions are used to calculate the net muscle torques exerted about the joints, from which muscle forces are determined using static optimization. Bottom Muscle excitations are the inputs and body motions are the outputs in forward dynamics. Muscle force (F ) is an intermediate product (i.e., output of the model for musculotendon dynamics). 

Serpas, F., Yanagawa, T., and Pandy, M. G. (2002). Forward-dynamics simulation of anterior cruciate ligament forces developed during isokinetic dynamometry. Computer Methods in Biomechanics and Biomedical Engineering, 5 33-43. 

The previously introduced method is now applied to a benchmark problem. The forward dynamics of a serial chain of n rigid bodies, connected by revolute joints, is solved with the recursive method, see Fig. 5. 

Other technique—for example, dynamic secondary ion mass spectrometry or forward recoil spectrometry—that rely on mass differences can use the same type of substitution to provide contrast. However, for hydrocarbon materials these methods attain a depth resolution of approximately 13 nm and 80 nm, respectively. For many problems in complex fluids and in polymers this resolution is too poor to extract critical information. Consequently, neutron reflectivity substantially extends the depth resolution capabilities of these methods and has led, in recent years, to key information not accessible by the other techniques. 

In literature, some researchers regarded that the continuum mechanic ceases to be valid to describe the lubrication behavior when clearance decreases down to such a limit. Reasons cited for the inadequacy of continuum methods applied to the lubrication confined between two solid walls in relative motion are that the problem is so complex that any theoretical approach is doomed to failure, and that the film is so thin, being inherently of molecular scale, that modeling the material as a continuum ceases to be valid. Due to the molecular orientation, the lubricant has an underlying microstructure. They turned to molecular dynamic simulation for help, from which macroscopic flow equations are drawn. This is also validated through molecular dynamic simulation by Hu et al. [6,7] and Mark et al. [8]. To date, experimental research had "got a little too far forward on its skis however, theoretical approaches have not had such rosy prospects as the experimental ones have. Theoretical modeling of the lubrication features associated with TFL is then urgently necessary. 

Sargent (SI) proposed a method of tearing in which all of the possible orderings of units in a block are considered, and dynamic programming is used to find the optimum order. The objective of the algirithm is to order the units into a sequence such that the minimum number of variables are associated with the output streams of units that feed preceeding units in the sequence. The objective is equivalent to ordering the units so that the maximum number of variables are associated with the feed forward streams. 

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