The Calculus of Variations for Double Integrals and It's    Application to Theories of Membranes and Elastic Plates
{'Code': '08080301', 'Directorate': {'Abbreviation': 'BIO', 'LongName': 'Direct For Biological Sciences'}, 'Division': {'Abbreviation': 'DBI', 'LongName': 'Div Of Biological Infrastructure'}}
{'SignBlockName': 'Alicia Armstrong', 'PO_EMAI': 'aarmstro@nsf.gov', 'PO_PHON': '7032924743'}
It is well recognized and increasingly studied that scientific                  instruments have transformed the nature of science.  The telescope              and microscope, for example, literally opened up whole new worlds for           scientific examination.  Another kind of instrument has also                    transformed science; but, because of the difficulties of examination            of these developments, these instruments are rarely examined with any           kind of historical sophistication.  These instruments are new                   techniques of mathematics.  While Newton's Principia was not written            using the new calculus (so his contemporaries could understand his              arguments) Newton's theory could not have been fully developed with             out calculus.  Similarly, Einstein's theory of general relativity               could not have been developed without new mathematical tools which he           had to learn in the early years of the second decade of this                    century.  These are the obvious examples, but there are many, many              more which simply have not been examined.  Professor Truesdell, an              award winning mathematician and scientist, has the technical skills             and a unique historical sensitivity to carry out the kind of analysis           of the role of mathematics in the development of science.  Under this           grant, he will examine a previously completely ignored area: the                history of the calculus of variations for double integrals.                     Variations of multiple integrals are essential tools of analysis for            contemporary theories of fluids, elastic solids and                             electromagnetism.  The use of multiple integrals in the mechanics of            continua enables us to comprehend and in part control the world                 around us today.  Studies thus are possible of the oceans, rivers,              lakes, tides and winds, acoustic vibrations, flight in the                      atmosphere, and earthquakes just to give a few examples.  The                   beginnings and the earliest application of variational principles to            double and triple integrals are due to Lagrange in his work between             1762 and 1811.  Lagrange's studies affected the development of the              general theory of elastic deformation in the 1830's by Navier,                  Poisson, and Cauchy.  They had an obvious effect on the research of             George Green and, through him, have influenced every branch of                  mathematical physics.  Professor Truesdell will examine this history            up through about 1830, tracing the mathematical development in detail           and describing its early application to mechanics and differential              geometry by Lagrange, Poisson, and Rodrigues.  This study will                  greatly enhance our understanding of the critical interaction of                mathematics and science--an interaction which has literally reshaped            every one of the sciences.
{'FirstName': 'Clifford', 'LastName': 'Truesdell', 'PI_MID_INIT': 'A', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Clifford A Truesdell', 'EmailAddress': None, 'NSF_ID': '000442551', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Johns Hopkins University', 'CityName': 'BALTIMORE', 'ZipCode': '212182608', 'PhoneNumber': '4439971898', 'StreetAddress': '3400 N CHARLES ST', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Maryland', 'StateCode': 'MD', 'CONGRESSDISTRICT': '07', 'CONGRESS_DISTRICT_ORG': 'MD07', 'ORG_UEI_NUM': 'FTMTDMBR29C7', 'ORG_LGL_BUS_NAME': 'THE JOHNS HOPKINS UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '1353', 'Text': 'Hist & Philosophy of SET'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8709401.xml'}