ABSTRACT
Wrist-pendulum systems are hybrid chemical-thermal-mechanical engines involving the following energy converting and partitioning sequence: Chemical energy is first converted to mechanical (kinetic) energy via an elaborate sarcomere cross-bridging; this mechanical energy is then systematically partitioned over external (mechanical work) processes and internal (thermodynamic) processes. The mechanisms underlying these processes are escapements that gate or channel the energy flows. The following questions are addressed: (i) What are the escapement requirements for the assembling processes, those that establish the parameters of oscillation? (ii) What are the escapement requirements for the sustaining processes, those that guarantee the subsistence of oscillations? (iii) What is the relation between mechanical processes and thermodynamic processes? (iv) What properties in the macroscopically observable states can be used to do the bookkeeping on the mechanical and thermo-dynamic processes? Finally, (v) What is the 'informational' description by which a subject parses the biomechanical work space (E,f) in search of 'preferred' comfort states? A theoretical construct is advanced for the physical basis of 'comfort' states. Central to the construct is an understanding of the lawful mixing of mechanical and thermodynamic processes under 329adiabatic conditions. Under these conditions, mechanical and thermodynamic processes are independent (orthogonal); the thermodynamic processes are invariant with changes in the mechanical processes. It is suggested that these steady-state manifestations in adiabatic conditions constitute a physical basis for 'comfort' that can 'orient' other trajectories of states in the (E,f) work space.
A second orienting property is associated with a Q-factor = 1. The Q-factor is a dimensionless scalar built out of the ratio of the (reversible) mechanical energy Em of a cycle and the (irreversible) thermodynamic energy Et, Q = [Em/Et]. The Q-factor provides a precise measure of the escapement requirements of a cycle. It identifies that portion of the total energy that must be put back into the cycle to restore its initial energy conditions. For example, a high Q-system (Q > > l) requires very little new escapement energy to return the energy state to its initial condition. For a perfectly conservative system Q = ∞, indicating that no additional energy is required to recover initial conditions. In contrast, as the Q-factor becomes smaller (Q≤1) the motion of the oscillator becomes dominated by internal thermodynamic processes. At Q = 1 the mechanical and thermodynamic energy flows are symmetric, resulting in a stable steady-state around which oscillatory parameters can orient.
The adiabatic invariant (H) and the quality factor (Q) are independent (orthogonal) variables that share a single common value. It is suggested that this value defines an attractor that orients globally oscillatory trajectories. The global attractor is defined at the intersection of the adiabatic and Q = 1 trajectories. All other states on these two trajectories constitute local "attractive" states that can bias or influence trajectories approaching the global attractor. Collectively, these locally "attractive" regions comprise a slow manifold (the regions are weakly attractive, the characteristic exponents are small). The slow manifold defines an intrinsic set of axes with the global attractor as origin. Information for orienting biomechanical oscillations is defined by vector flow patterns (morphologies) generated by variations in the oscillator's frequency and amplitude (energy). While the externally observed (E,f) work space appears quite complex, the internally-defined (H,Q) control space retains a simplicity that is invariant over variations in the number of mechanical degrees of freedom (muscle/joint complexes), growth, and artificial transformations. The invariance of the intrinsic coordinate space description over subsystem components addresses the problem of motor equivalence.
