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Numerical solution of optimal programming and control problems
Published in Arthur E. Bryson, Yu-Chi Ho, Applied Optimal Control, 2018
then on constrained arcs (S = 0), Equations (7.9.7) through (7.9.9) apply if we replace C(x,u,t) by S(q)(x,u,t). As in Section 7.9, the algorithm may be regarded as a split-interval algorithm, with the added complication that it deals with a multipoint boundary-value problem. For further discussion, see Bryson, Denham, and Dreyfus (1963), and Denham and Bryson (1964).
Estimation of maximum sprinting speed with timing gates: greater accuracy of 5-m split times compared to 10-m splits
Published in Sports Biomechanics, 2021
Santiago Zabaloy, Tomás T. Freitas, Jorge Carlos-Vivas, Julián C. Giráldez, Irineu Loturco, Fernando Pareja-Blanco, Javier Gálvez González, Pedro E. Alcaraz
The measurement of MSS provides useful information to practitioners, although the values must be valid and reliable to avoid misinterpretations. In this regard, the data reported here reveal an almost perfect correlation (r > 0.95) and a high level of agreement (i.e., ICC >0.96, CV <1.66%, and smallest detectable change <0.02 m/s, Table 2) between the observed and predicted values. Of note, r measures the strength of a relationship between two variables, not the agreement between them (Bland & Altman, 2010), thus, it is not possible to conclude that all three measures are in agreement. Roe et al. (2017) noted that both 10-Hz GPS and 10-m split times measured with timing gates provided valid measures of MSS over 40-m sprints in rugby players when compared to RG. These authors (Roe et al., 2017) reported that TG10 showed a small bias when estimating MSS compared with RG, but they did not report whether they were statistically different (8.78 ± 0.56 m/s vs. 8.57 ± 0.57 m/s for RG and TG10, respectively). Our findings showed even lower bias for TG5 (0.036 m/s) and TG10 (0.082 m/s) compared to RG, although significant differences were observed between TG10 and RG (p = 0.002). Furthermore, the analysis of the regression line between the data points on the Bland–Altman plot showed a very low coefficient of determination with a slope close to 0, meaning that the differences between instruments are constant for TG5 vs. RG regardless of the velocity magnitude (r2 = 0.01) (but not when RG was compared to TG10; r2 = 0.19). It should be noted that athletes can spend years of training to improve hundredths of seconds over short-sprints (Buchheit et al., 2014; Haugen & Buchheit, 2016; Sander et al., 2013). Thus, small bias resulting from the technology used may hamper the detection of actual changes in sprint performance. Therefore, practitioners should be aware that substantial differences may exist between the mean values of TG10 when compared to RG. It appears that the shorter the split interval (i.e., 5 m), the smaller the differences between the observed (RG) and the estimated MSS.