1. Mathematical Methods in Engineering (co-author Th. von Karman), McGraw-Hill Book Company, Inc., 505 pp., New York and London, 1940.
   [Foreign translations have been published in the following languages: French, Spanish, Portuguese, Russian, Turkish, Japanese, Polish, Hungarian, and Italian.]



2. Mechanics of Incremental Deformations, John Wiley & Sons, Inc., New York, 1965.
   [Theory of elasticity and viscoelasticity of initially stressed solids and fluids, including thermodynamic foundations and applications to finite strain.]



3. Variational Principles in Heat Transfer, Oxford University Press, 1970.
   [A unified Lagrangian analysis of dissipative phenomena.]

<Click here for the Scientific Articles>

Scientific Reports

Aeronautical Laboratory, California Institute of Technology

• No. 1. Vibration analysis of a wing carrying large concentrated weights. M. A. Biot, August 1941.



• No. 2. Flutter analysis of a wing carrying large concentrated weights. M. A. Biot, January 1942.
  


• No. 3. Electric network model of flexure torsion flutter. M. A. Biot and T. H. Wiancko, September 1941.
  


• No. 4. Flutter analysis of the B-24 C Twin Tail. M. A. Biot, August 1942.
  


• No. 5. Aerodynamic theory of the oscillating wing of finite Span. M. A. Biot and C.T. Boehnlein, September 1942.
  


• No. 6. Three dimensional aerodynamic theory applied to flutter analysis. M. A. Biot, December 1942.
  


• No. 7. Theory of electrical flutter predictor for three degrees of freedom. M. A. Biot and T. H. Wiancko, January 1943.

• Report 1. Chordwise divergence. The two-dimensional case. CAL/CM-427, December 1947.
  


• Report 2. An approximate treatment of some simple three-dimensional cases. CAL/CM-470, May 1948.
  


• Report 3. General method for the two-dimensional case. CAL/CM-506, September 1948.
  


• Report 4. Some exact solutions based on plate theory. CAL/CM-580, November 1949.
  


• Report 5. Stability of cantilever solid wings of symmetric cross-section and without sweep. CAL/CM-622, May 1950.
  


• Report 6. Solution of the divergence problem by the use of generalized co-ordinates. CAL/CM-730, March 1952.
  


• New expressions for the output of an FM Receiver with application to problems of interference (with S. Kaufman) CAL Rep. BE-745-T-134, August 1956.

• Dynamic stability of bombs and projectiles. NDRC Div. A. Sect. C, OSRD Contract OEMsr - 418, California Institute of Technology.
  

- Chapter I. Forces on a solid moving through an ideal fluid. July 1942.

- Chapter II. Stability derivatives in a real fluid. July 1942.

- Chapter III. Stability of the rectilinear trajectory in air and water neglecting gravity. September 1942.

- Chapter IV. Stability of the vertical fall. May 1943.


• The mechanism of water entry of projectiles. NDRC Div. A Sect. C, OSRD Contract OEMsr - 418, California Institute of Technology, September 1943.

• Aerodynamics of the oscillating airfoil in compressible flow (with S. N. Karp, S. S. Shu, H. Weil).
  

- I. Theory. USAF Tech. Rep. F-TR-1167-ND

- II. Graphical and numerical data. USAF Tech. Rep. F-TR-1195-NC (CDAM A-9-M Brown University).


• Investigation of aileron compressibility flutter (with Lee Arnold), USAF-AMC Wright Patterson AF Base, AF Tech. Rpt. No. 6341, August 1950 (declassified).
  


• Theory of armor penetration (with Lee Arnold), Contract DA-30-069- ORD-33, ballistic research laboratories, ordnance cors, Department of the Army.
  

- Report no. 1, February 1951.

- Report no. 2, January 1952.

- Report no. 3, January 1953.


• Short course for professors of mathematics and science, University College, London. "The function of mathematics in our civilization." April 1958, printed by Shell Development Company.

1. Linkage mechanism for steering of vehicles, Belgian patent 368, 623, March 15, 1930.
   [A linkage system which provides an exact kinematic solution to the problem of differential turning of the wheels for steering of automobiles and other vehicles.]



2. Radio guidance system for ships and aircraft, Belgian patent 372, 520, August 11, 1930.
   [(Dispositif emetteur recepteur realisant le reperage radioelectrique integral sans ondes dirigees.) The principle was described by M. A. Biot in a paper "Sur un procede de guidage des avions" published in l'Onde Electrique, vol. 9, no. 107, pp. 520-526, November 1930. Low frequency radio waves are transmitted from a main transmitter and its slave stations on synchronized frequencies. The transmitters are located about a hundred miles apart and the radio waves form a precise grid pattern of interference and phase difference. It provides an all-weather flight position picture for aircraft, sea-going ships, etc. The principle has received wide application and has been incorporated in the Bendix-Decca system now used throughout the world. Other trade names for these systems are Dectra, Delrac, and Navarho.]



3. Electrical synchronization of gun firing, through aircraft propeller disc, Belgian patent 37B, 042, March 16, 1931.
   [Achievement of precise synchronization in the firing of guns and machine guns through aircraft propeller disc by substituting an electrical firing system for the mechanical one.]



4. Aircraft turbo-compound engine, French patent 808, 770, November 4, 1935.
   [An aircraft engine combining a piston engine and a two-stage gas turbine. The patent claims are based on a detailed design carried out over a number of years in collaboration with L. Lvoff, director of "La Precision" in Brussels and now chief engineer of the Machine Tool Division of "La Brugeoise," Belgium. Specific weight and fuel consumption were predicted and fully confirmed by recent development. The principle was incorporated in the Wright Aeronautical compound engine. The invention was disclosed to technical and executive personnel of Wright Aeronautical and discussed at their Patterson, New Jersey, plant in June 1936.]



5. Flutter predicting apparatus, Maurice A. Biot and Thomas H. Wiancko, U.S. Patent Office 2448698, September 7, 1948. Application, October 21, 1944.
   [Electronic analog computer for the prediction of airplane flutter. An important novel feature was the design of a circuit which incorporates the effect of vorticity shedding of an oscillating wing.]



6. Hydraulic fracturing method to control vertical fracture height, J. L. Fitch, L. Masse, W. L. Medlin, M. A. Biot U.S. patent office 3851709, December 3, 1974.
   [Method of controlling height of fracture so that it does not extend vertically into adjacent formations on top and bottom.]



7. Harmonic oscillator for measuring dynamic elastic constants of rock materials. Maurice A. Biot, William L. Medlin, Lucien Masse, U.S. patent office 4 412 452, November 1, 1983.
   [A simple harmonic oscillator for use in measuring dynamic elastic constants of rock material samples includes a pair of masses vertically suspended by a pair of wires with the rock sample between them acting as a spring.]