Larry Silverberg


  • 919-515-5665
  • Engineering Building III (EB3) 3118
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Daily Calendar for Scheduling Appointments

I teach MAE 789 4D Dynamics.The course is a modern treatment of dynamics with a focus on the engineering challenges with systematically integrating disciplines, scales, and phases. In the modern treatment the physical process is represented by a four-dimensional field. An emphasis is placed on theoretical and computational issues of integrative modelling. At the undergraduate level, I recently introduced a new course – MAE 320 Mechatronics – in which learning takes place through a hands-on, self-directed experience.

Outside of work, I enjoy basketball and spending time with family and friends.

One of the challenges that faces engineering is with dynamic modelling that systematically integrates disciplines (mechanical, electrical, and thermodynamic), scale (small and large), and phase (gaseous, liquid, and solid states). Another challenge that faces engineering is with algorithm development for non-physical processes, like for autonomous operation and exploration. If you are interested in dynamic system modelling and algorithm development, see the project list at the bottom of this page and feel free to contact me for more information.

The first ongoing project, being led by Thomas Powers (PhD candidate) is the development and demonstration of a new autonomous path planning algorithm for small-class unmanned aerial vehicles that produces what is called “Lumbered Flight,” that is, the lazy motion that birds are observed to use to conserve energy. This is a joint effort with Dr. Gopalarathnam.

The second ongoing project deals with developing computer-aided design/exploration tools for early engineering education. The goal is to develop CAD apps for core classes in the AE and ME curricula (statics, dynamics, solids, heat transfer, and vibration). This is a joint project with Drs. Eischen and Batastilli, funded by MATHWORKS, with development work performed by Will Morrow and Sean MaGuire.

The third ongoing project, which is being performed by undergraduate students and directed by me and Dr. Chau Tran, studies the dynamics of basketball. Through the simulation of millions of trajectories, the goal is to understand best practices in shooting, like of the free throw and the bank shot. Current work, being performed by Chris Laue, focuses on answering the age-old question “Who is the superior of the sexes when it comes to the free throw shot?”

The fourth ongoing project, which is being performed by Taylor Reininger (MS Candidate), is developing a modal learning methodology for multi-legged robotic systems.??

The fifth ongoing project, which is being performed by Skyler Edenhart-Pepe (MS Candidate), is developing real-time image processing methods for aerial vehicles.??

Project List – Applied Research

1. About Autonomous Systems: In these projects the students develop algorithms that enhance autonomy. They include:

(a) algorithms that allow a single user to operate a system of flight vehicles,

(b) algorithms for lumbered flight, and

(c) learning algorithms for articulated systems.

2. About Exploration Apps for Early Engineering: In these projects the student develops a discipline-specific computer app for early STEM (science, technology, engineering, and mathematics). The tools are for classroom use at the sophomore and junior college levels. They are used to check answers, solve more complex problems than can be solved by hand, and overall to provide an exploratory platform for improved learning and design. Several of the discipline-specific computer apps are listed below:

(a) Rigid-body collisions app, (b) Potential flow app, (c) Thermal expansion feature in truss and frame apps, (d) Deformation feature in potential flow app (aeroelasticity), (e) Electrostatics app, (f) Electromagnetics app, (g) circuitry app, (h) Radiation feature in truss and frame apps

Project List – Basic Research in Computational Methods

1. About scale: Where does the particle scale end and where does the thermal scale begin? In this project the student constructs the simplest particle system for which particles move “randomly” which occurs when thermal properties are obtained. The study translating these behaviors into scaling heuristics for computational models.? ?

2. About scale: Can you generate the dry friction laws? In this project the student constructs a system of bound particles (a block) that slide over a rough surface. The system generates the dry friction laws. The study translating these behaviors into scaling heuristics for computational models.? ?

3. About scale: The normal probability function exp(-kr^2), used in statistical problems, and the 1/r function, used in deterministic problems, both satisfy the wave equation. That being said, can the normal probability function be substituted for the 1/r function to avoid the r = 0 singularity in 1/r? In this project, the student studies this substitution. The study translating these behaviors into scaling heuristics for computational models.? ?

4. About numerical analysis: Wave solutions are simplified by neglecting near-field effects giving rise to the so-called far-field approximation. Can numerical analysis be simplified (and how) by neglecting far-field effects to produce the “near-field approximation”? In this project, the student looks at the errors associated with the “near-field approximation.” The study translating these behaviors into scaling heuristics for computational models.? ?

5. About 4D: In 4D, force is a geometric quantity. In this project, the student develops a graphical way of visualizing the 4D force. This is used for visualization purposes to assist with understanding 4D principles.?



Engineering Mechanics

Virginia Polytechnic Institute


Engineering Mechanics

Virginia Polytechnic Institute


Engineering Mechanics

Virginia Polytechnic Institute

Research Description

Dr. Silverberg's research is in dynamic system modeling and algorithm development for autonomy and exploration.


Cellular growth algorithms for shape design of truss structures
Tschida, C. E., & Silverberg, L. M. (2013), Computers and Structures, 116, 1-6.
Optimal Targets for the Bank Shot in Mens Basketball
Silverberg, L. M., Tran, C. M., & Adams, T. M. (2011), Journal of Quantitative Analysis in Sports, 7(1).
Autonomous soaring: The montague cross-country challenge
Edwards, D. J., & Silverberg, L. M. (2010), Journal of Aircraft, 47(5), 1763-1769.
Control of underwater vehicles in full unsteady flow
Levedahl, B. A., & Silverberg, L. (2009), IEEE Journal of Oceanic Engineering, 34(4), 656-668.
Fourier series of half-range functions by smooth extension
Morton, J., & Silverberg, L. (2009), Applied Mathematical Modelling, 33(2), 812-821.
Characterizing hydrodynamic loads in full unsteady flow
Silverberg, L., & Levedahl, B. (2008), AIAA Journal, 46(12), 3159-3163.
Optimal release conditions for the free throw in men's basketball
Tran, C. M., & Silverberg, L. M. (2008), Journal of Sports Sciences, 26(11), 1147-1155.
Basic experiments in PID control for engineers
Silverberg, L. (Larry), Tran, Chau. (2005), Boston : Pearson/Custom Publishing.
Transpermanent magnetics using alternating uniform linear stacks
Silverberg, L., & Duval, L. (2005), Journal of Mechanical Design (New York, N.Y. : 1990), 127(4), 679-687.
Autonomous coordination of aircraft formations using direct and nearest-neighbor approaches
Silverberg, L., & Levedahl, B. A. (2005), Journal of Aircraft, 42(2), 469-477.

View all publications via NC State Libraries


CAD Apps for Core Courses in AE and ME Curricula: Bridge Funding 
The MathWorks, Inc.(1/01/16 - 5/31/17)
Angelfish: Initial Planning and Project Management
Defense Advanced Research Projects Agency (DARPA)(6/19/14 - 1/31/16)
NCSU Autonomy
US Army - Army Research Office(8/01/14 - 8/31/15)
CAD Apps for Core Courses in AE and ME Curricula
The MathWorks, Inc.(5/16/13 - 5/14/15)
Building Design Apps for Early Engineering Education
National Science Foundation (NSF)(1/15/11 - 7/31/13)
Advancement of Thermal Sensing and Centering Algorithms
US Navy-Office Of Naval Research(1/01/10 - 5/15/10)
Principles of Autonomous Soaring
US Navy-Office Of Naval Research(1/01/09 - 12/31/09)
Autonomous Soaring Algorithm
US Navy-Office Of Naval Research(10/01/07 - 12/31/08)
CPATH CB: Computing Across Curricula
National Science Foundation (NSF)(7/01/07 - 9/30/10)
Real-Time Synthesis of Unsteady Hydrodynamic Loads from Measurements on the Hull Surface
US Navy-Office Of Naval Research(5/01/06 - 2/28/10)