New explicit solutions to the incompressible Navier-Stokes equations in R2 \ {0} are determined, which generalize the scale-invariant solutions found by Hamel. These new solutions are invariant under a particular combination of the scaling and rotational symmetries. They are the only solutions invariant under this new symmetry in the same way as the Hamel solutions are the only scaleinvariant s...

A Hamel basis is a set a, ô, c, • • • of real numbers such that if x is any real number whatsoever then x may be expressed uniquely in the form aa+(3b+yc + • • • where a, j8, 7, • • • are rational numbers of which only a finite number are different from zero. Since each of these sums is formed from a finite number of nonzero terms and the coefficients a, /3, 7, • • • are rational and therefore ...

Abstract The Boltzmann–Hamel (BH) equations are central in the dynamics and control of nonholonomic systems described terms quasi-velocities. rigid body is a classical example such systems, it well-known that BH-equations Newton–Euler (NE) when twists as It further known NE-equations Euler–Poincaré, respectively, reduced Euler–Lagrange on SE (3) using body-fixed or spatial representation twists...

We show that an infinite-dimensional complete linear space X has: • a dense hereditarily Baire Hamel basis if |X| ≤ c; • a dense non-meager Hamel basis if |X| = κ = 2 for some cardinal κ. According to Corollary 3.4 of [BDHMP] each infinite-dimensional separable Banach space X has a non-meager Hamel basis. This is a special case of Theorem3.3 of [BDHMP], asserting that an infinite-dimensional Ba...