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Purpose To evaluate whether a change in fitness is associated with academic outcomes in New York City (NYC) middle school students using longitudinal data, and to evaluate whether this relationship is modified by student household poverty. Methods This was a longitudinal study of 83,111 NYC middle school students enrolled between 2006–07 and 2011–12. Fitness was measured as a composite percentile based on three fitness tests and categorized based on change from the previous year. The effect of the fitness change level on academic outcomes, measured as a composite percentile based on state standardized mathematics and English Language Arts test scores, was estimated using a multilevel growth model. Models were stratified by sex and additional models were tested stratified by student household poverty. Results For both girls and boys, a substantial increase in fitness from the previous year resulted in a greater improvement in academic ranking than was seen in the reference group (girls: .36 greater percentile point improvement, 95% confidence interval: .09-.63; boys: .38 greater percentile point improvement, 95% confidence interval: .09-.66). A substantial decrease in fitness was associated with a decrease in academics in both boys and girls. Effects of fitness on academics were stronger in high-poverty boys and girls than in low-poverty boys and girls. Conclusions Academic rankings improved for boys and girls who increased their fitness level by >20 percentile points relative to other students. Opportunities for increased physical fitness may be important to support academic performance.

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n-n being the degrees-of-freedom of the system at hand--inverse dynamics and order n 3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system's accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.Downloaded 23 Nov 2007 to 203.199.213.67. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm I=k and 1VIi is given in Eq. (23a). Note that, the 6 × 6 matrix, xI~rk, has a recursive relation, whose substitution, along with that of Mr, Eq.

A decomposition of the manipulator inertia matrix is essential, for example, in forward dynamics, where the joint accelerations are solved from the dynamical equations of motion. To do this, unlike a numerical algorithm, an analytical approach is suggested in this paper. The approach is based on the symbolic Gaussian elimination of the inertia matrix that reveal recursive relations among the elements of the resulting matrices. As a result, the decomposition can be done with the complexity of order n; O(n)-n being the degrees of freedom of the manipulator-, as opposed to an O(n 3) scheme, required in the numerical approach. In turn, O(n) inverse and forward dynamics algorithms can be developed. As an illustration, an O(n) forward dynamics algorithm is presented.