The dynamics associated with the impact of the crutch with the ground is an important\ud topic of research, since this is known to be the main cause of mechanical energy\ud loss during swing-through gait. In this work, a multibody system representing a subject\ud walking with crutches is used to investigate the behavior of two different contact models,\ud impulsive and continuous, used for impact analysis. In the impulsive (discrete) approach,\ud the impact interval is considered to be negligible and, therefore, the system configuration\ud is constant. The postimpact state is directly obtained from the preimpact one through algebraic\ud equations. In the continuous approach, the stiffness and dissipation characteristics of\ud the contact surfaces are modeled through nonlinear springs and dampers. The equations of\ud motion are integrated during the impact time interval to obtain the postimpact state, which,\ud in principle, can differ from that obtained by means of the impulsive approach. Although\ud both approaches have been widely used in the field of biomechanics, we have not found any\ud comparative study in the existing literature justifying the model chosen for impact analysis.\ud In this work, we present detailed numerical results and discussions to investigate several\ud dynamic and energetic features associated with crutch impact. Based on the results, we compare\ud the implications of using one contact model or the other.Postprint (published version

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We present a theoretical study and experimental results for an acoustic multiscattering one-dimensional system made of cylindrical tubes of different diameters whose lengths follow a Cantor-like structure. Homothetic acoustical features and forbidden bands as well as wave trapping phenomena are reported.

Traditionally the description of the acoustical behavior of a bore has been done in the frequency domain through the acoustical impedance or the reflection coefficient. Whenever the time-domain response of it (impulse response, reflection function) has been needed, it has usually been obtained through the Fourier transform (FT) of the corresponding frequencydomain function. However, there are a number of cases in which this approach is unsuitable because the FT leads to noncausal functions which cannot be understood physically as impulse responses or reflection functions. In such cases the time-domain calculation is unavoidable. This calculation leads to exponentially growing functions which obviously do not accept an FT. This article presents the time-domain calculation of the main basic functions (reflection and transmission functions associated with a single discontinuity, impulse responses of anechoic bores) which are needed to obtain the input reflection function and the impulse responses of a bore. The analytical calculation of an application case is also presented.

In unidimensional acoustical systems, the impulse response h(t) at the input section, which describes the pressure evolution originated at this section by the introduction of a flow unit impulse through it, relates pressure p(t) and flow u(t) at the input section by means of the convolution product p=h*u. If damping and radiation are small, it is interesting to find other functions of faster decay than h(t) in order to improve the convolution convergence. As alternatives to h(t), this article studies the impulse responses h′(t) and h″(t), which correspond to the modified systems that result when coupling the original acoustical system input section to a cylindrical anechoic termination and a conical anechoic termination, respectively. These functions h′(t) and h″(t) are related to the plane-wave reflection function Rp−(t) and spherical-wave reflection function Rs−(t), respectively. The comparison of these three impulse responses shows that the use of h′(t) and h″(t), though of faster decay than h(t) in principle, is not always advisable. For conical bores with small truncation, the convolution with h′(t) may lead to numerical instability more easily than that with h(t). On the other hand, the impulse response h″(t) turns out to be divergent for certain geometrical duct configurations, and thus it is useless as a kernel function in a convolution in these cases.

The human body is an over-actuated multi-body system, as each joint degree of freedom can be controlled by more than one muscle. Solving the force-sharing problem (i.e. finding out how the resultant joint torque is shared among the muscles actuating that joint) calls for an optimization process where a cost function, representing the strategy followed by the central nervous system to activate muscles, is minimized. The main contribution of the present study has been the particular formulation of that cost function for the case of the pathological gait of a single subject suffering from anterior cruciate ligament rupture. Our hypothesis was that the central nervous system does not weight equally the muscles when trying to compensate for a lower limb injury during gait (in contrast to what is the usual practice for healthy gait where all muscles are weighted equally). This hypothesis is supported by the fact that muscle activity in injured individuals differs from that of healthy subjects. Different functions were tested until we finally came out with a cost function that was consistent with experimental electromyography measurements and inverse dynamics results for a subject suffering this particular pathology.

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The multiconvolution algorithm ͓Martínez et al., J. Acoust. Soc. Am. 84, 1620-1627 ͑1988͔͒ to calculate the impulse response or reflection function of a musical instrument air column has proved to be useful, but it has the limitation that the spacing between discontinuites is constrained to be some multiple of c⌬t ͑for phase velocity c and time step ⌬t͒. This paper presents an improved method, the continuous-time interpolated multiconvolution ͑CTIM͒, where such a limitation has been removed. The response of an air column, modeled as an arbitrary one-dimensional acoustic waveguide constructed using cylindrical or conical bore segments with viscothermal damping and tone-hole discontinuities, is obtained through continuous-time convolutions between analytical reflection and transmission functions and discrete-time pressure signals. The arbitrary spacing between discontinuites is accounted for by interpolation of the discrete-time pressure signals. Many musical instrument air columns possess tone holes that are opened or closed so that tones of different pitches are produced. A time-domain calculation is presented of the acoustic responses of tone-hole discontinuities that may be open or closed. The resulting reflection and transmission functions are well suited for use in the CTIM. INTRODUCTIONThe simulation of the acoustical behavior of wind instruments requires the dynamical description of the main two parts of such systems, the bore and the driver, and their mutual interaction. As the driver is essentially a nonlinear system, it is always described in the time domain through a differential equation. For that reason, even if the bore behaves, under playing conditions, approximately as a linear system, so that its description can be made either in time domain or in frequency domain, it is a time-domain response ͓usually its input impulse response h(t)͔ that is used when studying the bore-to-driver feedback.There are mainly two techniques to calculate h(t): either as the inverse Fourier transform ͑FT͒ of the corresponding frequency response ͓the input impedance Z()͔ or directly in the time domain. The first technique implies all the inconveniences associated with numerical FTs. To overcome these difficulties, Martínez et al. ͑1988a͒ proposed a direct method in the time domain through a numerical multiconvolution process which has proven to be useful. However, that algorithm has a limitation: the time step ⌬t used in the calculation has to be small enough so that each of the spacings between discontinuities along the bore ͑changes in diameter, in taper, open and closed tone holes etc.͒ is an exact multiple of c⌬t ͑where c is the phase velocity of sound in air neglecting dissipation͒. Smith ͑1992͒ worked with a similar idea to simulate wave propagation in strings. There is a brief discussion of a band-limited interpolation method to treat the case where ⌬t is not an exact multiple of c⌬t, but there is no discussion of how this method is generalized to model wave propagation in conical waveguides with discontinuities r...