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Phys. (1972) pp. 975-978. [55] L. I. Y, 1959. [56] M. J. SEWELL, "Mechanical demonstration of buckling and branching,"BIMA (1983) pp. 61-66. [57] D. B. SHAFFER, "Maximum range of a projectile in a vacuum," Amer. J. Phys. (1956) pp. 585-586. [58] S. K. STEIN, "Kepler's second law and the speed of a planet "AMM (1967) pp. 1246-1248. [59] J. J. STOKER, Nonlinear Vibrations, Interscience, New York, 1950. [60] J. L. SYNGE AND B. A. Y, 1959. [61] J. L. SYNGE, "Problems in mechanics," AMM (1948) pp. 22-24.

Since the times of the traverses will in general be different, we cannot have both T\ ^ T2 and T2 ^ T}. A problem related to part (i) is that the aircraft flies the same closed path twice with the second time around in the reverse direction. All the other conditions of the problem are the same as before except that the wind field need not be irrotational. Then the totaf time of flight is an increasing function of k (/cW ^ 0). In this case if the aircraft only flew one loop, the time of flight could be less then the time of flight without wind (just consider a whirlwind).

51] F. R. Y, 1962. Y, 1962. [53] A. S. RAMSEY, Dynamics I, II, Cambridge University Press, Cambridge, 1946. [54] R. M. ROSENBERG, "On Newton's law of gravitation," Amer. J. Phys. (1972) pp. 975-978. [55] L. I. Y, 1959. [56] M. J. SEWELL, "Mechanical demonstration of buckling and branching,"BIMA (1983) pp. 61-66. [57] D. B. SHAFFER, "Maximum range of a projectile in a vacuum," Amer. J. Phys. (1956) pp. 585-586. [58] S. K. STEIN, "Kepler's second law and the speed of a planet "AMM (1967) pp. 1246-1248.