Frank Baginski

Department of Mathematics
The George Washington University
Hall of Government  Room 224
2115 G Street NW
Washington, DC 20052

Phone: (202) 994-6269
Fax: (202) 994-6760

Spring 2014

Math 6330 Section 10 - Ordinary Differential Equations
  Tu & Th 09:35-10:50 in 1957 E, Room 310

 Information on Careers in Mathematics

Previous Courses

 Math 6340 (formerly 221) Modern Partial Differential Equations

 Math 231 Topics in Applied Mathematics

Research Interests

The advancement of materials and technology  in thin light-weight films has generated great interest in
deployable space structures for a variety of applications, including  inflatable  rovers, inflatable antennas,
airbags to  cushion  landings, aerobots, planetary and terrestrial  balloons.  Current research interests
focus on the development of a mathematical model for high altitude balloons used by NASA to support
research in the upper atmosphere.  To take full advantage of current balloon technology or develop new
balloon designs, it is important to have a valid mathematical model for estimating maximum stresses
and strains that are experienced by the balloon film prior to launch and during its ascent to float altitude.
The problem is complicated by the fact that the balloon film can fold back upon itself and wrinkle
(see the images below). The balloon problem generates a wealth of challenging
mathematical problems in differential geometry,  the mechanics of membranes,  and direct  methods in the calculus of variations.

A large scientific balloon at launch
An undesired equilibrium configuration at float altitude

Recent work on large super pressure pumpkin balloons,  focusing on questions of stability,  sensitivity
analysis, the formulation of  undesired stable equilibria (see above), and the deployment problem.
Long term success  of the pumpkin balloon for NASA requires a thorough understanding of the
phenomenon of multiple stable equilibria.  For an ultra long duration balloon (ULDB) mission of 100 days or
longer, there is a need for design criteria  that will enable the designer to arrive at structurally efficient designs
while providing sufficient margins against the occurrence of  instability, and in  the case of a visco-elastic film
also accounting  for the service lifetime configuration changes of the balloon.

For more on scientific ballooning see the following links:

 NASA Balloon Program Office

 NASA Columbia Scientific Balloon Facility

Selected Publications