Larry M. Silverberg: Biographical Narrative

Silverberg is a dynamicist and educator, recognized in physics for introducing the term fragment of energy (See Silverberg below major contributions 2008 – 2021).


Silverberg attended Virginia Polytechnic and State University (1976-1983). He studied under the dynamicist Leonard Meirovitch from 1977 until receiving the PhD in engineering mechanics in 1983. Silverberg joined the faculty at North Carolina State University in 1984. Over his career, Silverberg is credited with developing a large number of applied and theoretical methods that advanced the foundation of ordinary and spacetime dynamics.


Larry M. Silverberg was born 5 November 1957, in New Canaan, Connecticut. He was one of four children by his mother Marian Stern and father Jeroll Silverberg, who was a prominent lawyer in Connecticut. Larry has a twin brother David Silverberg, and two sisters Ellen Silverberg and Phyllis Koren. When young, Larry’s mother married Robert Pinsly and she adopted his children – Bernard (Buzzy) Pinsly and James Pinsly. In 1971, Marian and Robert moved to Israel, taking with them Bernard, James, Larry and David. Larry and David lived in Israel until 1976. Between the ages of 15 and 18, Mar (Mr.) Ben Nathan taught Larry Silverberg mathematics. Silverberg credits Ben Nathan with giving him a strong mathematical foundation to build on. In 1976, Silverberg entered Virginia Polytechnic Institute and State University (now Virginia Tech). He conducted research under the guidance of the renowned dynamicist Leonard Meirovitch from 1977 until receiving the PhD in engineering mechanics in 1983. Silverberg credits Meirovitch with giving him a strong foundation in dynamics. In 1987, Silverberg married Debbie Due and their daughter, Corinne Silverberg, was born in 1989. Early in his personal life, Silverberg enjoyed competitive basketball and later enjoyed studying basketball dynamics with his colleague Dr. Chau Tran. Today, Silverberg and his wife Debbie enjoy a quiet life in Apex, North Carolina.   

 Major Contributions

1983 – 1994, Modal control

  • Meirovitch and Silverberg 1983: Extended the Independent Modal-Space Control (IMSC) method to systems with viscous damping, circulatory forces and aerodynamic forces.
  • Silverberg and Yunis 1986: Showed that compromises in structural feedback control are endemic to their formulations, whether formulated as underdetermined, as uniquely determined, or as overdetermined.
  • Silverberg 1986: Developed the uniform damping principle for control of distributed systems, showing that the controller is independent of stiffness, control forces proportional to the mass distribution, decentralized, and approximates the solution to the globally optimal control problem.
  • Silverberg and Morton 1989: Showed inherent properties of natural control (IMSC) – fuel consumption that is near-optimal, and open-loop and closed-loop frequencies and modes that are nearly identical.
  • Silverberg 1990: Argued that a new area of civil engineering in space is emerging, and that motion control of space structures is fundamentally a civil engineering problem.
  • Weaver and Silverberg 1992: Introduced a method of applying discrete, decentralized actuators at nodes of distributed systems.
  • Silverberg and Washington 1994: Developed a method of varying the shape of thin membrane space-based antennas to maximize far-field power received.
Selected references

Meirovitch and Larry M. Silverberg 1983 “Control of non-self-adjoint distributed-parameter systems,” The 22nd IEEE Conference on Decision and Control, 1983, pp. 281-285, doi: 10.1109/CDC.1983.269842.

Larry M. Silverberg and Isam S. Yunis 1990 “The compromise inherent in structural feedback control,” Applied Mathematical Modelling, Volume 14, Issue 7, July, p. 362-369.

Larry M. Silverberg 1986 “Uniform Damping Control of Spacecraft,” Journal of Guidance, Control, and Dynamics, Vol. 9, Issue 2, p. 221-227, March, 10.2514/3.20093

Larry. M. Silverberg and Mark Morton 1989 “On the nature of natural control,” Vibration, Acoustics, Stress, and Reliability. Oct., 111(4): 412-422

Larry M. Silverberg 1990 “Motion control of structures,” J. Aerospace Engineering, Vol 3, Issue 4,

Weaver, Jr, and Larry M. Silverberg 1992 “Node control of uniform beams subject to various boundary conditions,” J. Appl. Mech. Dec., 59(4): 983-990,

Larry M. Silverberg and Gregory Washington 1994 “Modal control of reflector surfaces using far-field power measurements,” Microwave and Optical Technology Letters (ISSN 0895-2477), vol. 7, no. 12, August, p. 588-593.

1989 – 1993 Modal identification

  • Norris and Silverberg 1989: Introduced a method of identifying modal quantities, exploiting spatial and temporal orthogonality.
  • Silverberg and Kang 1989: Developed a new method of modal identification based on a variational problem that seeks stationary values of a quotient.
  • Norris and Silverberg 1990: Extended their modal identification method for self-adjoint systems to gyroscopic systems.
  • Norris, Kahn, Silverberg, and Hedgecock 1993: Conducted experiments with their method of modal identification for self-adjoint structures.
Selected references

Mark A. Norris and Larry M. Silverberg 1989, “Modal Identification of self-adjoint distributed-parameter systems,” Earthquake Engineering & Structural Dynamics, Vol. 18, Issue 5 p. 633-642, July,

Larry M. Silverberg and S. Kang 1989, “Variational Modal Identification of Conservative Non-gyroscopic Systems,” J. Dynamic Systems, Measurement, and Control, June, 111(2): 160-171,

Mark A. Norris and Larry M. Silverberg 1990, “Modal Identification of Gyroscopic Distributed-Parameter Systems,” AIAA journal, Vol. 28, Issue 12, 2104-2109, December, DOI: 10.2514/3.10528

M. A. Norris, S. P. Kahn, L. M. Silverberg, and C. E. Hedgecock 1993, “Temporal correlation method for modal identification of lightly damped structures,” Sound and Vibration, Vol. 162, Issue 1, 22, March, p. 137-146.

1991 – 1996 Fuel-optimal (impulse) control 

  • Foster and Silverberg 1991: Developed a minimum-fuel heuristic for control of flexible structures
  • Redmond and Silverberg 1992: Compared optimal bang-bang, optimal continuous, and optimal impulse control on benchmark problems showing optimal impulse is 25% to 35% more fuel-efficient.
  • Redmond, Meyer, and Silverberg 1993: Conducted an experiment that demonstrates impulse damping control of a vertically suspended 16 foot long beam
  • Silverberg 1992: Developed impulse damping control algorithms for distributed spacecraft systems.
  • Silverberg and Meyer 1993: Conducted an experiment that demonstrates fuel-optimal slewing in the horizontal plane of a hinged-free beam
  • Redmond and Silverberg 1994: Presented an exact solution to the fuel-optimal propulsive control problem and a near optimal solution that consumes 8% more fuel than the optimum.
  • Meyer and Silverberg 1996: Conducted a landmark experiment that demonstrates fuel-optimal control of a space-like structure having five rigid-body modes and a multitude of flexible-body modes.
Selected references

A. Foster, L. M. Silverberg 1991 “On-Off decentralized control of flexible structures,” J. Dynamic Systems, Measurement, and Control, March, 113(1): 41-47,

Redmond and Larry M. Silverberg 1992 “Fuel consumption in optimal control,” Guidance, Control, and Dynamics, Vol 15, No. 2, March-April, p. 424-430.

Redmond, J. L. Meyer, and L. M. Silverberg 1993, “Impulse Damping Control of an Experimental Structure,” Sound and Vibration, Vol. 160, Issue 1, p. 179-186, January, 10.1006/jsvi.1993.1015
Larry M. Silverberg 1992, “Light Impulsive Damping of Spacecraft Exhibiting Normal Mode Behavior,” Guidance, Control, and Dynamics, Vol 15, No. 1, p. 114-120.

Larry M. Silverberg and John L. Meyer 1993 “Fuel-optimal slewing of an experimental hinged-free beam,” J. guidance, control, and dynamics, Vol 16, No. 6, November-December, p. 1162-1168. 

Redmond and Larry M. Silverberg 1994 “An exact solution to the fuel-optimal propulsive control of a tutorial structure,” Sound and Vibration, Vol 171, Issue 1, March, p. 23-33.

L. Meyer and Larry M. Silverberg 1996 “Fuel-optimal Propulsive Maneuver of an experimental structure exhibiting space-like dynamics,” guidance, control, and dynamics, Vol 19, No. 1, January-February, p. 141-149.

1991 – 1994 Protection against intercontinental missiles

Program director – Larry M. Silverberg

Sponsor – NASA Johnson Space Center

  • Directed a program whose purpose was to calibrate the space-command’s worldwide array of ground-based radar to be able to see incoming intercontinental missiles
  • Developed a method and apparatus wherein the space shuttle would release spheres of known physical size and albedo into low-earth orbit in order to calibrate ground-based radars and optical telescopes with small objects.

Program chronology

  • 1991 academic year (fall and spring): 40 NCSU students divide into 4 teams, and fabricate 4 competing prototype designs
  • 1991 summer: Flight systems of two of the four designs are fabricated (OEM-6 and OE-6 designs). NASA selects the OE-6 design
  • 1991 November: Orbiter Ejector OE-6 delivered to NASA JSC
  • NASA certification:
    • Vibration testing – February 1992
    • Thermal Vacuum Testing – April 1992
    • EMI (Electromagnetic Interference) Testing – June 1992
  • July 1992: Delivery to Kennedy Space Center (KSC)
  • December 1992: Orbiter Ejector flown aboard Shuttle flight STS-47. Experiment fails due to dead battery.
  • December 1993: Orbiter Ejector re-flown successfully on shuttle flight STS-53.
  • August 1994: Orbiter Ejector flown successfully on shuttle flight STS-60.
  • November 1994: Program established at NASA JSC to continue calibration under oversight of the department of defense.

Sphere Ejection Parameters

Ejection Order

Diameter (inches)


Exit Velocity (m/s)






440 SS





440 SS





440 SS





440 SS





6061-T6 AL





6061-T6 AL

Selected references

Larry M. Silverberg 1992 “Design and flight hardware fabrication of the OE-6 orbiter ejector,” AIAA Space Programs and Technologies Conference, NASA 92-1282, January

1996 – 2000 Electrodynamic methods and apparatuses

  • Larry M. Silverberg 1992: Developed a thin membrane space-based antenna with high pointing accuracy
  • Silverberg and Weaver 1996: Formulated the governing equations for dynamics and control of electrostatic structures.
  • Silverberg and Stanley 1996: Experiment demonstrated highly flexible adaptable antenna
  • Silverberg 1998: Developed a method of opening/closing blinds encased in insulted glass by electrostatic means.
  • Stanley and Silverberg 1999: Experiment of electrostatically-shaped reflector showed pointing and bean-width control of a radiating surface.
  • Kiefer, Silverberg and Gonzolez 2001: Studied the heat transfer in electrostatically actuated window blinds.
  • Silverberg and Duval 2003: Developed a method of switching the states of permanent magnets through on-board magnetization.
  • Silverberg and Farmer 2004: Showed that trans-permanent actuation is well-suited for spacecraft pointing, shape control, and deployment applications.
Selected references

Larry M. Silverberg 1992 “Electrostatically Shaped membranes,” US Patent 5307082A

Larry M. Silverberg and L. Weaver Jr. 1996 “Dynamics and control of electrostatic structures,” Applied Mechanics, June 1996, 63(2): 383-391,

Larry M. Silverberg and Robert Stanley 1996 “Space-based electrostatic antenna design with pointing and beam width control,” Spacecraft and Rockets, Vol 33, No. 6, November-December, p. 843-847.

Larry M. Silverberg 1998 “Electrostatically positioned blind Insert for insulated glass,” US Patent 5850861

Robert J. Stanley, Larry M. Silverberg 1999 “Paraboloidally shaped antenna possessing pointing and bean-width control,” Spacecraft and Rockets, Vol. 36, No. 5, September-October, p. 736-744.

Scott F. Kiefer, Larry M. Silverberg, and Manoel L. Gonzolez 2001 “Electrostatically actuated window blinds,” Vol. 50, Issue 4, March, p. 229-248.

Larry M. Silverberg and Luis Duval 2003 ” Analysis of Trans-permanent Magnetic systems,” J. Dynamic, Systems, Measurement, and Control, March, 125(1): 143-146.

Larry M. Silverberg and Dan Farmer 2004 “Trans-permanent magnetic actuation for spacecraft pointing, shape control, and deployment,” Spacecraft and Rockets, Vol 41, No. 6, November-December, p. 1051-1055

1992 – 2013 Robotics and systems

  • Silverberg and Levedahl 2005: Developed a direct approach and explained the inherent problems with the nearest-neighbor approach in aircraft formations.
  • Silverberg and Gardiner 1992: Developed an informal gradient method of controlling motion of a robot that resembles a water skier.
  • Tschida and Silverberg 2013: Introduced a novel approach to truss structure shape design, drawing inspiration from biological processes.
Selected references

Larry M. Silverberg and John Richard Gardiner 1992 “Control of the motion of a headless water skier,” Mathematics and Computers in Simulation, Vol 34, Issue 2, August, p. 163-181.

Larry M. Silverberg and Blaine A. Levedahl 2005 “Autonomous coordination of aircraft formations using direct and nearest-neighbor approaches, J. Aircraft, Vol. 42, No. 2, March-April, p. 469-477.

Colin E. Tschida and Larry M. Silverberg 2013 “Cellular growth algorithms for shape design of truss structures,” Computers & Structures, Vol.116, 15 January, p. 1 – 6.

2009 – 2010 Unmanned vehicles

  • Levedahl and Silverberg 2009: Developed a general formulation for control of underwater vehicles in full unsteady flow.
  • Edwards and Silverberg 2010: Introduced a method for unmanned aerial vehicles to locate and fly in thermals.
Selected references

Blaine A. Levedahl and Larry M. Silverberg, “Control of Underwater Vehicles in Full Unsteady Flow,” in IEEE Journal of Oceanic Engineering, vol. 34, no. 4, pp. 656-668, Oct. 2009, doi: 10.1109/JOE.2009.2027798.

Daniel J. Edwards and Larry M. Silverberg, “Autonomous Soaring: The Montague Cross-Country Challenge,” J. Aircraft, Vol. 47, No. 5, September-October 2010, p. 1763-1769.

2008 – 2021 Spacetime dynamics

  • Silverberg 2008: Published a monograph on spacetime dynamics
  • Silverberg and Eischen 2020: Introduced a new field theory formulation that predicts precisely the same precession of Mercury and the same bending of light as general relativity.
  • Silverberg and Eischen 2021: Introduced the theory of Spacetime Impetus
Selected references

Larry M. Silverberg, Unified Field Theory, Wiley-VCH, 2008, ISBN-13: 978-3527407880

Larry M. Silverberg and Jeffrey W. Eischen, “On a new field theory formulation and spacetime adjustment that predict the same precession of Mercury and the same bending of light as general relativity,” Physics essays, 33(4), 489-512.

Larry M. Silverberg and Jeffrey W. Eischen, “Theory of Spacetime Impetus,” Physics essays, 34(4) (2021),

2003 – 2011 Basketball dynamics

  • Silverberg, Tran, and Adcock 2003: Developed a general formulation for the dynamics of the basketball shot that can be used to improve individual shooting and statistical accuracy of the release.
  • Tran and Silverberg 2008: Found the optimal release conditions for the free throw in men’s basketball.
  • Silverberg, Tran, and Adams 2011: Showed that the optimal targets for the bank shot are observable at the intersection of a vertical pole behind the backboard and a V-shaped pattern on the backboard.
  • Fisher 2018 develops the physics of the free throw with a special book chapter by Silverberg
Selected references

Larry M. Silverberg, Chau Tran, and Kit Adcock 2003 “Numerical analysis of the basketball shot,” J. Dynamic Systems, Measurement, and Control, December, 125(4): 531-540,

Chau M. Tran & Larry M. Silverberg 2008 “Optimal release conditions for the free throw in men’s basketball,” Journal of Sports Sciences, 26:11, 1147-1155, DOI: 10.1080/02640410802004948

Larry M. Silverberg, Chau M Tran, and Taylor M. Adams 2011 “Optimal Targets for the Bank Shot in Men’s Basketball,” Journal of Quantitative Analysis in Sports: Vol. 7: Issue 1, Article 3. DOI:10.2202/1559-0410.1299

Bob J. Fisher, Straight Shooter, Telemachus Press, 2018, ISBN 9781948046138