Net force

Abstract: Models of earthquake sources that have no volume change, no net force, and no net torque as criteria for the radiation of first motions, have five degrees of freedom in their spatial orientation. The usual double-couple model has only three degrees of freedom. The most general source of high-frequency seismic motions must be a linear combination of a double couple and another source called the compensated linear-vector dipole. A radiation pattern of amplitudes of first motions on the focal sphere cannot be uniquely decomposed into the radiation patterns due to the two sources.

Abstract: The relation of cellular activity in the motor cortex to the direction of two-dimensionalisometric force was investigated under dynamic conditions in monkeys. A task was designedso that three force variables were dissociated:the force exerted by the subject, thenet force, and the change in force. Recordings of neuronal activity in the motor cortexrevealed that the activity of single cells was directionally tuned and that this tuning wasinvariant across different directions of a bias force. Cell activity was not related to thedirection of force exerted by the subject, which changed drastically as the bias forcechanged. In contrast, the direction of net force, the direction of force change, and thevisually instructed direction all remained quite invariant and congruent and could be thedirectional variables, alone or in combination, to which cell activity might relate.

Abstract: Recent work on the aerodynamics of flapping flight reveals fundamental differences in the mechanisms of aerodynamic force generation between fixed and flapping wings. When fixed wings translate at high angles of attack, they periodically generate and shed leading and trailing edge vortices as reflected in their fluctuating aerodynamic force traces and associated flow visualization. In contrast, wings flapping at high angles of attack generate stable leading edge vorticity, which persists throughout the duration of the stroke and enhances mean aerodynamic forces. Here, we show that aerodynamic forces can be controlled by altering the trailing edge flexibility of a flapping wing. We used a dynamically scaled mechanical model of flapping flight (Re approximately 2000) to measure the aerodynamic forces on flapping wings of variable flexural stiffness (EI). For low to medium angles of attack, as flexibility of the wing increases, its ability to generate aerodynamic forces decreases monotonically but its lift-to-drag ratios remain approximately constant. The instantaneous force traces reveal no major differences in the underlying modes of force generation for flexible and rigid wings, but the magnitude of force, the angle of net force vector and centre of pressure all vary systematically with wing flexibility. Even a rudimentary framework of wing veins is sufficient to restore the ability of flexible wings to generate forces at near-rigid values. Thus, the magnitude of force generation can be controlled by modulating the trailing edge flexibility and thereby controlling the magnitude of the leading edge vorticity. To characterize this, we have generated a detailed database of aerodynamic forces as a function of several variables including material properties, kinematics, aerodynamic forces and centre of pressure, which can also be used to help validate computational models of aeroelastic flapping wings. These experiments will also be useful for wing design for small robotic insects and, to a limited extent, in understanding the aerodynamics of flapping insect wings.