@article{silverberg_tran_2024, title={High performance computing of the nonlinear dynamics of a basketball}, volume={6}, ISSN={["1573-269X"]}, DOI={10.1007/s11071-024-09833-z}, journal={NONLINEAR DYNAMICS}, author={Silverberg, Larry M. and Tran, Chau M.}, year={2024}, month={Jun} }
 @article{silverberg_tran_laue_2018, title={Gender comparison in consistency in the basketball free throw by an event-driven approach}, volume={21}, ISSN={["1460-2687"]}, DOI={10.1007/s12283-018-0276-z}, number={4}, journal={SPORTS ENGINEERING}, author={Silverberg, Larry M. and Tran, Chau M. and Laue, Christopher}, year={2018}, month={Dec}, pages={333–340} }
 @article{silverberg_tran_adams_2011, title={Optimal Targets for the Bank Shot in Men's Basketball}, volume={7}, ISSN={["1559-0410"]}, DOI={10.2202/1559-0410.1299}, abstractNote={The purpose of this study was to gain an understanding of the bank shot and ultimately determine the optimal target points on the backboard for the bank shot in men’s basketball. The study used over one million three-dimensional simulations of basketball trajectories. Four launch variables were studied: launch height, launch speed, launch angle, and aim angle. The shooter’s statistical characteristics were prescribed to yield a 70 percent free throw when launching the ball seven feet above the ground with 3 Hz of back spin. We found that the shooter can select a bank shot over a direct shot with as much as a 20 percent advantage. The distribution over the court of preferences of the bank shot over the direct shot was determined. It was also shown that there is an aim line on the backboard independent of the shooter’s location on the court. We also found that at 3.326 inches behind the backboard, there exists a vertical axis that aids in finding the optimal target point on the backboard. The optimal target point is the crossing of the vertical axis and the aim line that is in the shooter’s line of sight.}, number={1}, journal={JOURNAL OF QUANTITATIVE ANALYSIS IN SPORTS}, author={Silverberg, Larry M. and Tran, Chau M. and Adams, Taylor M.}, year={2011}, month={Jan} }
 @article{tran_silverberg_2008, title={Optimal release conditions for the free throw in men's basketball}, volume={26}, ISSN={["1466-447X"]}, DOI={10.1080/02640410802004948}, abstractNote={Abstract The purpose of this study was to determine the optimum release conditions for the free throw in men's basketball. The study used hundreds of thousands of three-dimensional simulations of basketball trajectories. Five release variables were studied: release height, release speed, launch angle, side angle, and back spin. The free throw shooter was assumed to shoot at 70% and to release the ball 2.134 m (7 ft) above the ground. We found that the shooter should place up to 3 Hz of back spin on the ball, should aim the ball towards the back of the ring, and should launch the ball at 52° to the horizontal. We also found that it is desirable to release the ball as high above the ground as possible, as long as this does not adversely affect the player's launch consistency.}, number={11}, journal={JOURNAL OF SPORTS SCIENCES}, author={Tran, Chau M. and Silverberg, Larry M.}, year={2008}, pages={1147–1155} }
 @article{tran_southward_2006, title={A sensor placement strategy for the hybrid adaptive feedforward observer}, volume={128}, ISSN={["0022-0434"]}, DOI={10.1115/1.2196421}, abstractNote={A sensor placement technique is proposed for implementing the hybrid adaptive feedforward observer. The observer is a conventional dynamic observer augmented with an adaptive feedforward component for estimating the effect of persistent, nonstationary disturbances. The placement technique searches for the least possible number of sensors that satisfy two criteria, the observability of the plant, and the lowest condition number of the error dynamic system's state matrix. Demonstration was performed on a one-dimensional acoustic duct. The results show that the proposed technique is an effective guideline for identifying the optimal sensor locations.}, number={2}, journal={JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME}, author={Tran, CM and Southward, SC}, year={2006}, month={Jun}, pages={449–452} }
 @book{basic experiments in pid control for engineers_2005, ISBN={053697571X}, publisher={Boston : Pearson/Custom Publishing}, year={2005} }
 @article{silverberg_tran_adcock_2003, title={Numerical analysis of the basketball shot}, volume={125}, ISSN={["1528-9028"]}, DOI={10.1115/1.1636193}, abstractNote={This paper numerically analyzes the dynamics of the basketball shot. The focus of the paper is on the development of a general formulation for the dynamics of the shot beginning when the ball leaves the shooter’s hand and ending when the shot is made or missed. The numerical analysis developed in this paper can be used to conduct a parametric study of the dynamics of the basketball shot, which in turn, can be used to improve individual shooting and team strategy. The individual skill level of the shooter enters the formulation through the statistical accuracy of the release. The paper then shows how to determine the shooter’s probability of making a given shot.}, number={4}, journal={JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME}, author={Silverberg, L and Tran, C and Adcock, K}, year={2003}, month={Dec}, pages={531–540} }
 @article{tran_southward_2003, title={Stability and convergence of a hybrid adaptive feedforward observer}, volume={26}, ISSN={["0731-5090"]}, DOI={10.2514/2.5036}, number={1}, journal={JOURNAL OF GUIDANCE CONTROL AND DYNAMICS}, author={Tran, CM and Southward, SC}, year={2003}, pages={189–192} }
 @article{tran_southward_2002, title={A Virtual Sensing method for tonal ANVC systems}, volume={124}, ISSN={["0022-0434"]}, DOI={10.1115/1.1435642}, abstractNote={Virtual Sensing (VS) is considered to be an extension for feedforward Active Noise and Vibration Control (ANVC) systems when, for example, it is desired to minimize the response at one or more spatial locations where it is either physically impossible or undesirable to place an actual error sensor. In this context, VS is an estimation technique for predicting the appropriate system response using available measurements and a dynamic system model. A hybrid adaptive feedforward observer is proposed which has the ability to overcome the limitations of conventional dynamic observer designs. The hybrid observer utilizes a conventional dynamic observer augmented with an adaptive feedforward element for estimating the effect of the persistent disturbance. For simplicity, we restrict this development to a single tonal disturbance for which a coherent reference is assumed available. It will be appreciated that this technique may be extended to handle disturbances that contain multiple tones as well as broadband noise, as long as suitable reference signals are available. Numerical simulations and real-time experiments were performed on a one-dimensional acoustic duct. The results demonstrate that the hybrid adaptive feedforward observer is an effective method for predicting the virtual sensor response in an ANVC system.}, number={1}, journal={JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME}, author={Tran, CM and Southward, SC}, year={2002}, month={Mar}, pages={35–40} }