Question

Let's consider a rigid system with three particles. Masses of these particles
m1 = 3 kgs, m2 = 4 kg, m3 = 2 kgs, and their positions are (1, 0, 1), (1, 1, -1) and
Let it be (1, -1, 0). Locations are given in meters

a)What is the inertia tensor of the system?
b)What are the main moments of inertia?
c)what are the principal axes

Answer 1

Aut. given that А чi gid ym uu de pashu mои оf The parh. m, - зк m, - чK8 elimetion on of ma - 24 (1,-1,0) 1 Т). Та (+, +7) (1,1,-1) 4 m Then Intenia Tensoy of the Jystem- é mo Iry: + { mi rigi Iur 9+(m(0) + m, (0) + m, (-)] от, • [o+ия) - 1) 2 [m*) Iy2 = Izy - Mi Yizi (to) + (-1) + m, (оо] — ч() - m2 Izs I2 = mi rizi 3 | т (1) + m(-) + 0 о) (3) - ч) - - к9 m2 2

Ruincipal area Ixxa m ( x'+y? + 2'- x'] me gº+2) [MiCu) + m2(1+1) + mg (0) ( 3x1 + + 2) uX2 13 3 +6 +2= kg .m2 Iyy m(x²+2²) ( 3 (1+1) + 4(1+1) + 2(11) 16 kg.me + 3x2 + ux2 + 2 6 + 8 +2 Izz m(x² + y) * [3(01 + 3 (1 + 4 (1+1) + 2(1+1)] kom? 15 + 3 + 8 + 4 = (6) main moment of Ineutia: - it can be about it own axis. For for about 3 lg 11,0,1) its own aris mass x perpendi ular distance 3 (1+1) 7 6 kym? for m2 ukg (1,1,-1) it will be at anis , U(1+1) any og kynn for m3 about zaais ☆ 2 (1+1) y 4