By Livija Cveticanin
This ebook bargains with the matter of dynamics of our bodies with time-variable mass and second of inertia. Mass addition and mass separation from the physique are handled. either features of mass version, continuous and discontinual, are thought of. Dynamic homes of the physique are got utilizing ideas of classical dynamics and in addition analytical mechanics. merits and drawbacks of either techniques are mentioned. Dynamics of continuing physique is followed, and the features of the mass version of the physique is incorporated. certain cognizance is given to the effect of the reactive strength and the reactive torque. The vibration of the physique with variable mass is gifted. One and levels of freedom oscillators with variable mass are mentioned. Rotors and the Van der Pol oscillator with variable mass are displayed. The chaotic movement of our bodies with variable mass is mentioned too. To help studying, a few solved sensible difficulties are included.
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Extra info for Dynamics of Bodies with Time-Variable Mass
For ϕ = π/2, virtual work is zero. If ϕ = 0, virtual work is a product of the intensities of the impulse of the resultant force and of the virtual velocity of Fr the mass centre of the body, δ A J = J Fr δv S . For straight angle (ϕ = π), it is Fr δ A J = −J Fr δv S . 82) is virtual work of the impulse J M of the torque M δ AM = J M δ . Virtual work is defined as the inner product of the impulse torque J M and of the virtual angle velocity δ . 3 Modified Lagrange’s Equations Let us introduce generalized velocities q˙i , where i = 1, 2, .
3 case 5). Absolute velocity of mass centre of the remainder body is equal to dragging velocity of S1 before body separation. Angular velocity of the remainder body is equal to angular velocity of the initial body before separation. 2. If motion of the initial body and of the separated body is translatory with velocity v S (relative velocity u is zero), velocity of mass centre of the remainder body is also v S . This result was previously obtained by Meshchersky (1897), for continual mass variation of the translatory moving particle.
Rotor rotates with constant angular velocity . Moment of inertia of the disc is I S for axis z in mass centre S. It is assumed that a part of the body with mass m is separated. It causes change in motion of the remainder body. Aim of this example is to determine motion of the remainder body after mass separation. Analysis is divided into three parts: 1. Motion of the initial rotor. 2. Velocity and angular velocity variation due to body separation. 3. Motion of the remainder body after mass separation.
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