Abstract We revisit and present new linear spaces of explicit solutions to incompressible Euler Navier–Stokes equations on ${{{\mathbb{R}}}}^n$, as well the rotating Boussinesq ${{{\mathbb{R}}}}^3$. cast these are superpositions certain plane waves arbitrary amplitudes that also solve nonlinear by constraints wave vectors flow directions. For $n\leqslant 3$, examples for generalized Beltrami fl...

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...

Euler gave recipes for converting alternating series of two types, I and II, into equivalent continued fractions, i.e., ones whose convergents equal the partial sums. A condition we prove irrationality a fraction then allows easy proofs that \(e,\sin 1\), primorial constant are irrational. Our main result is that, if type II to simple fraction, sum transcendental its measure exceeds 2. We const...

The objective of this manuscript is to develop, for the first time, a mathematical model prediction buckling, postbuckling, and nonlinear bending imperfect bio-inspired helicoidal composite beams with rotation angle. equilibrium integrodifferential equations (curved) are derived from Euler–Bernoulli kinematic assumption. differential integral quadrature method (DIQM) Newton-iterative employed e...