The equation $det(i - \lambda i_3) = 0$ represents the characteristic polynomial that is used to determine the eigenvalues of the inertia tensor matrix for a rigid body. This mathematical expression connects the moments and products of inertia, providing insight into how an object's mass distribution affects its rotational behavior. The eigenvalues obtained from this equation are critical for understanding the principal moments of inertia, which dictate how a spacecraft will respond to applied torques during rotation.
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