inertiamatriisi

Inertiamatriisi, also known as the inertia tensor, is a mathematical object used in physics, particularly in classical mechanics, to describe the distribution of mass of a rigid body. It quantifies how the body's resistance to angular acceleration varies depending on the axis of rotation.

The inertia tensor is a 3x3 symmetric matrix. Its components are calculated based on the body's mass elements and their positions relative to a chosen coordinate system. Specifically, the diagonal elements represent the mass moment of inertia about each of the coordinate axes, while the off-diagonal elements account for the product of inertia, which describes how mass is distributed relative to pairs of axes.

The inertia tensor is fundamental for understanding rotational motion. When a body rotates, its angular momentum and kinetic energy are related to its inertia tensor and its angular velocity. The inertia tensor simplifies calculations involving torque and angular acceleration through Euler's equations of motion. It is a key concept in areas such as robotics, aerospace engineering, and the study of celestial mechanics. The choice of the coordinate system affects the numerical values of the inertia tensor, but it can be transformed between different coordinate systems.