Lawrence Silverberg Miller, L. R., Silverberg, L. M., Eischen, J. W., & Miller, S. R. (2024). How Schwarzschild could have discovered and fixed the problem with his metric. PHYSICS ESSAYS, 37(1), 74–79. https://doi.org/10.4006/0836-1398-37.1.74 Silverberg, L. M., & Eischen, J. W. (2023, September 8). Trajectory of a Spacecraft When It Passes by a Gravitational Body During Interstellar Travel. JOURNAL OF SPACECRAFT AND ROCKETS, Vol. 9. https://doi.org/10.2514/1.A35684 vanVuuren, M., vanVuuren, R., Silverberg, L. M., Manning, J., Pacifici, K., Dorgeloh, W., & Campbell, J. (2023). Ungulate responses and habituation to unmanned aerial vehicles in Africa's savanna. PLOS ONE, 18(7). https://doi.org/10.1371/journal.pone.0288975 Mollik, T., Kennedy, S., Ul Shougat, M. R. E., Li, X., Fitzgerald, T., Echols, S., … Perkins, E. (2022, June 2). Discrete element method simulator for joint dynamics: a case study using a red-tailed hawk's hallux digit. MULTIBODY SYSTEM DYNAMICS, Vol. 6. https://doi.org/10.1007/s11044-022-09828-x Coppola, S., & Silverberg, L. M. (2021). Isotropic packing algorithm for particle simulations. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 122(17), 4698–4708. https://doi.org/10.1002/nme.6742 Powers, T. C., Silverberg, L. M., & Gopalarathnam, A. (2020). Artificial Lumbered Flight for Autonomous Soaring. JOURNAL OF GUIDANCE CONTROL AND DYNAMICS, 43(3), 553–566. https://doi.org/10.2514/1.G004397 Silverberg, L. M., & Eischen, J. W. (2020). On a new field theory formulation and a space-time adjustment that predict the same precession of Mercury and the same bending of light as general relativity. PHYSICS ESSAYS, 33(4), 489–512. https://doi.org/10.4006/0836-1398-33.4.489 Zhu, D., Pritchard, E. G. D., & Silverberg, L. M. (2018). A New System Development Framework Driven by a Model-Based Testing Approach Bridged by Information Flow. IEEE SYSTEMS JOURNAL, 12(3), 2917–2924. https://doi.org/10.1109/JSYST.2016.2631142 Silverberg, L. M., Tran, C. M., & Laue, C. (2018). Gender comparison in consistency in the basketball free throw by an event-driven approach. SPORTS ENGINEERING, 21(4), 333–340. https://doi.org/10.1007/s12283-018-0276-z Tschida, C. E., & Silverberg, L. M. (2013). Cellular growth algorithms for shape design of truss structures. COMPUTERS & STRUCTURES, 116, 1–6. https://doi.org/10.1016/j.compstruc.2012.10.006 Silverberg, L. M., Tran, C. M., & Adams, T. M. (2011). Optimal Targets for the Bank Shot in Men's Basketball. JOURNAL OF QUANTITATIVE ANALYSIS IN SPORTS, 7(1). https://doi.org/10.2202/1559-0410.1299 Edwards, D. J., & Silverberg, L. M. (2010). Autonomous Soaring: The Montague Cross-Country Challenge. JOURNAL OF AIRCRAFT, 47(5), 1763–1769. https://doi.org/10.2514/1.c000287 Levedahl, B. A., & Silverberg, L. (2009). Control of Underwater Vehicles in Full Unsteady Flow. IEEE JOURNAL OF OCEANIC ENGINEERING, 34(4), 656–668. https://doi.org/10.1109/JOE.2009.2027798 Morton, J., & Silverberg, L. (2009). Fourier series of half-range functions by smooth extension. APPLIED MATHEMATICAL MODELLING, 33(2), 812–821. https://doi.org/10.1016/j.apm.2007.12.009 Silverberg, L., & Levedahl, B. (2008). Characterizing Hydrodynamic Loads in Full Unsteady Flow. AIAA JOURNAL, 46(12), 3159–3163. https://doi.org/10.2514/1.36626 Tran, C. M., & Silverberg, L. M. (2008). Optimal release conditions for the free throw in men's basketball. JOURNAL OF SPORTS SCIENCES, 26(11), 1147–1155. https://doi.org/10.1080/02640410802004948 Silverberg, L., & Levedahl, B. A. (2005). Autonomous coordination of aircraft formations using direct and nearest-neighbor approaches. JOURNAL OF AIRCRAFT, 42(2), 469–477. https://doi.org/10.2514/1.6868 Basic experiments in PID control for engineers. (2005). Boston : Pearson/Custom Publishing. Silverberg, L., & Duval, L. (2005). Transpermanent magnetics using alternating uniform linear stacks. JOURNAL OF MECHANICAL DESIGN, 127(4), 679–687. https://doi.org/10.1115/1.1897743 Kiefer, S., Silverberg, L., & Gonzalez, M. (2004). A case study of prototyping methods and design for manufacture: electrostatic window blinds. JOURNAL OF ENGINEERING DESIGN, 15(1), 91–106. https://doi.org/10.1080/0954482021000050820 Silverberg, L., & Farmer, D. (2004). Transpermanent magnetic actuation for spacecraft pointing, shape control, and deployment. JOURNAL OF SPACECRAFT AND ROCKETS, 41(6), 1051–1055. https://doi.org/10.2514/1.1350 Silverberg, L., & Duval, L. (2003). Analysis of trans-permanent magnetic systems. JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME, 125(1), 143–146. https://doi.org/10.1115/1.1543553 Silverberg, L., Tran, C., & Adcock, K. (2003). Numerical analysis of the basketball shot. JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME, 125(4), 531–540. https://doi.org/10.1115/1.1636193 Kiefer, S. F., Silverberg, L. M., & Gonzalez, M. L. (2001). Electrostatically actuated window blinds. Journal of Electrostatics, 50(4), 229–248. https://doi.org/10.1016/s0304-3886(00)00038-3 Silverberg, L., & Thrower, J. P. (2001). Marks' mechanics problem-solving companion. New York: McGraw-Hill. Stanley, R. J., & Silverberg, L. M. (1999). Paraboloidally shaped antenna possessing pointing and beam-width control. JOURNAL OF SPACECRAFT AND ROCKETS, 36(5), 736–744. https://doi.org/10.2514/2.3487 Silverberg, L., & Washington, G. (1999). Weighted-residual discretization for uniform damping and uniform stiffening of structural systems. JOURNAL OF GUIDANCE CONTROL AND DYNAMICS, 22(4), 614–618. https://doi.org/10.2514/2.7638 Silverberg, L. (1998). Comment on "conjecture about orthogonal functions" - Reply. JOURNAL OF GUIDANCE CONTROL AND DYNAMICS, Vol. 21, pp. 189–190. https://doi.org/10.2514/2.4223 Wang, H. L., Eischen, J. W., & Silverberg, L. M. (1998). On control and optimization of elastic multilink mechanisms. COMPUTERS & STRUCTURES, 67(6), 483–502. https://doi.org/10.1016/s0045-7949(98)00060-1 Silverberg, L. (1997). Conjecture about orthogonal functions. JOURNAL OF GUIDANCE CONTROL AND DYNAMICS, 20(1), 198–202. https://doi.org/10.2514/2.4021 Washington, G. N., & Silverberg, L. (1997). Uniform damping and stiffness control of structures with distributed actuators. JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME, 119(3), 561–565. https://doi.org/10.1115/1.2801294 Silverberg, L. M. (1994). Electrostatically shaped membranes. Washington, DC: U.S. Patent and Trademark Office.