Dynamic behavior of a circular shaft with geometrical nonlinearity and constant spin, subjected to periodic axial load is investigated. The case of parametric combination resonance is studied. Extension of shaft center line is the source of nonlinearity. The shaft has gyroscopic effect and rotary inertia but shear deformation is neglected. The equations of motion are derived by extended Hamilto...

Topological mechanical metamaterials are artificial structures whose unusual properties are protected very much like their electronic and optical counterparts. Here, we present an experimental and theoretical study of an active metamaterial--composed of coupled gyroscopes on a lattice--that breaks time-reversal symmetry. The vibrational spectrum displays a sonic gap populated by topologically p...

It has been established by now that the problem of the absolute stability originates from a paper of B.V. Bulgakov published in 1942. The engineering application generating the problem was the so called gyroscopic pendulum, with various applications in stabilization of ships, aircrafts or armored cars. Even if nowadays the technical implementation of this device might be completely different, t...

A geometric formulation for stabilization of systems with one degree of underactuation which fully solves the energy shaping problem for these system is given. The results show that any linearly controllable simple mechanical system with one degree of underactuation is stabilizable by energy shaping, even in the absence of gyroscopic force, via a closed-loop metric which is not necessarily posi...

The maintenance of large-scale differential rotation in stellar convective regions by rotationally influenced convective stresses also drives large-scale meridional flows by angular– momentum conservation. This process is an example of “gyroscopic pumping”, and has recently been studied in detail in the solar context. An important question concerns the extent to which these gyroscopically pumpe...

Sagnac effect has been studied in terms of Gyroscopic system both Lorentz frame as well flat Einstein frame. The equivalence principle used to determine the phase shift due pseudo force transformation from rotating earth stationary A polychromatic broadband source considered for discussion. Langevin-Landau-Lifschitz metric during incorporation General theory relativity. square type sagnac inter...