Summary
A study of three-dimensional solenoidal-lamellar vector fields whose vector magnitude is constant along a vector-line. Polynomial relationships are obtained as necessary conditions on the vector-field parameters.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hill M. J. M.,On the Classification of the Integrals of Linear Partial Differential Equations of the First Order, Proc. London Math. Soc., Series 2, Vol. 16 (1917), 219–272.
Hill M. J. M.,On the Use of a Property of Jacobians to determine the Character of any Solution of an Ordinary Differential Equation of the First Order, or of a Linear Partial Differential Equation of the First Order, Proc. London Math. Soc., Series 2, Vol. 20 (1921), 85–92.
Hamel G.,Potentialströmungen mit konstanter Geschwindigkeit, Sitzgsber, preuss. Akad. Wiss., Phys.-math. (1937) Kl 5–20.
Piaggio H. T. H.,Special Integrals of Lagrange's Linear Partial Differential Equation, J. London Math. Soc., Vol.13 (1938), 264–272.
Piaggio H. T. H.,Geometry of Special Integrals of Lagrange's Equation, J. London Math. Soc., Vol. 14 (1939), 228.
Prim R. C.,Steady rotational flow of ideal gases, J. Rational Mech. Anal., 1 (1952), 425–497.
Howard L. N.,constant Speed Flows, Doctoral dissertation, M. S. in Princeton University Library (1953).
Truesdell C. and R. A. Toupin,The Classical Field Theories, Handbuch der Physik III, Berlin-Göttingen-Heidelberg, Springer (1960).
Marris A. W.,Hill's Jacobian Theorem, Rend. Circ. Matem. di Palermo, Serie II, Tomo XVII (1968), 257–282.
Shiau J. F.,A Study on a Theorem of Hamel, Doctoral dissertation, M. S. in Georgia Institute of Technology Library (1972).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Marris, A.W., Shiau, J.F. Hamel's theorem: The three polynomial integrals. Rend. Circ. Mat. Palermo 22, 185–216 (1973). https://doi.org/10.1007/BF02851096
Issue Date:
DOI: https://doi.org/10.1007/BF02851096