Experimental examination of the gyroscopic and rotary inertia effects on the chatter boundary in a milling operation is the chief aim of this article. The equations of motion of the tool vibration are derived based on Timoshenko beam theory and Hamilton principle by considering gyroscopic moment, rotary inertia, velocity-dependent process damping and radial immersion effect. For a range of dept...

The inverse eigenvalue problem of constructing symmetric positive semidefinite matrixD written as D ≥ 0 and real-valued skew-symmetric matrix G i.e., G −G of order n for the quadratic pencilQ λ : λMa λ D G Ka, whereMa > 0,Ka ≥ 0 are given analytical mass and stiffness matrices, so that Q λ has a prescribed subset of eigenvalues and eigenvectors, is considered. Necessary and sufficient condition...

The effect of random inputs on the movement of systems of solid bodies was investigated by many authors, see, for example, [1]. The paper deals with the analysis of the equations of gyroscopic systems under the influence of random forces. The possibility of the replacement of the equations of motion by the corresponding precessional equations is investigated. This approach is widespread in mech...

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...

The paper studies gyroscopic obstacle avoidance for autonomous vehicles. The goal is to obtain a simple controller that steers around obstacles and stabilizes to a desired state. The approach is applicable under the assumption that the obstacles are convex and that the control inputs can generate the required steering forces. This work extends the existing gyroscopic obstacle avoidance methodol...

The paper presents the theoretical basis for modal analysis of a general nonconservative system. The modal analysis uses only real modes in terms of the displacements as well as velocity coordinates and converts the system to a real, uncoupled, second-order form. This is the first time that such a transformation has been presented in the literature. Earlier works presented modal analysis in the...

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We study the phenomenon of gyroscopic precession and the analogues of inertial forces within the framework of general relativity. Covariant connections between the two are established for circular orbits in stationary spacetimes with axial symmetry. Specializing to static spacetimes, we prove that gyroscopic precession and centrifugal force both reverse at the photon orbits. Simultaneous non-re...