moment of inertiaWe describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous medium model, where all characteristics and fields are defined everywhere in the volume but they follow some generalized equations which are derived...
structures, subjected to dynamic loads - inertia terms, added to equationsdynamics of mass/spring systems - free motion insight, into nature of structural dynamics or vibrationaxial vibration of a slender bar - solutions based on differential equation...
The analytical solution is verified by comparing analytical results with numerical solutions of the original nonlinear equations of motion. The stability criterion shows that the motion is stable if the spin axis is the principal axis of the maximum moment of inertia. The effect of the damper ...
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This inertia tensor is a 3x3 matrix and since the other terms in this equation are defined in absolute coordinates the inertia tensor is defined in absolute coordinates, this means that the elements of the inertia tensor may be time dependant. This makes the equations very complicated, so to ...
17 Planar Kinetics of a Rigid Body: Force and Acceleration 17.1 Mass Moment of Inertia 17.2 Planar Kinetic Equations of Motion 17.3 Equations of Motion: Translation 17.4 Equations of Motion: Rotation about a Fixed Axis 17.5 Equations of Motion: General Plane Motion ...
According to Newton's law and the momentum moment theorem, the dynamic equations of the aircraft under the body frame14, 15, 16 can be written as follows:(1)Fx=mu̇+qw-rvFy=mv̇+ru-pwFz=mẇ+pv-qu(2)Mx=ṗIx-ṙIxz+qr(Iz-Iy)-pqIxzMy=q̇Iy+pq(Ix-Iz)+(p2-r2)Ix...
The dynamics of elastic systems coupled with rotating bladed-rotors is rich and complex, and the blade number may have an influence on the in-vacuo system dynamics. This paper aims to model its nonlinear dynamics in-vacuo and study the effects of blade number on its dynamics. To this end,...
The output update function compute_y returns y (argument 1) and uses 3 input arguments: the state vector x, the input vector u, and five of the six parameters (the air resistance CA is not needed) encoded in p: /* Output equations. */ void compute_y(double *y, double *x, double...
For a corotating frame of reference, the equations of motion are (29)ζ¨=2Ωη˙-∂2Φ∂r2ζ for the radial equation and (30)η¨+2Ωζ˙=0 for the angular equation. Therefore, there is a characteristic frequency (31)k2=2Ω2+∂2Φ∂r2 which is the epicyclic frequency we ...