Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetryâ€¦ (More)

W e desire to p lan a n optimal trajectory for an airplane moving at a constant velocity f r o m some starting point and orientation t o some final point and orientation. The problem is formulated asâ€¦ (More)

A Goursat flag is a chain Ds âŠ‚ Dsâˆ’1 âŠ‚ D1 âŠ‚ D0 = TM of subbundles of the tangent bundle TM such that corank Di = i and Diâˆ’1 is generated by the vector fields in Di and their Lie brackets. Engel,â€¦ (More)

We analyze the natural process of flipping a coin which is caught in the hand. We show that vigorously flipped coins tend to come up the same way they started. The limiting chance of coming up thisâ€¦ (More)

W e describe a new solution to the three-body problem (C. Moore [1993], Chenciner and Montgomery [2001]) and motivate its discovery. We also sketch its existence proof, which is based on the directâ€¦ (More)

We show that any bounded zero-angular-momentum solution of the Newtonian three-body problem suffers infinitely many syzygies (collinearities) provided that it does not suffer a triple collision. Ourâ€¦ (More)

A global formula for Poisson brackets on reduced cotangent bundles of principal bundles is derived. The result bears on the basic constructions for interacting systems due to Sternberg and Weinstei nâ€¦ (More)