Abstract
The inertia tensor of a tetrahedron is composed of its moments of inertia. This study presents explicit exact formulas for the moments of inertia of a 3-D tetrahedron as simple polynomials of its vertex coordinates.
Highlights
The knowledge of the inertia tensor of a solid is of fundamental importance in many branches of applied mathematics, computer science and mechanics
If the tetrahedron inertia tensor can be calculated with respect to the same reference system, the inertia tensor for the entire solid can be obtained as the sum of those inertia tensors
Formulas have been given for the integration of polynomials over a tetrahedron [6,7,8,9] and references therein, in the literature no explicit expression has been given for the inertia tensor in terms of the vertex coordinates
Summary
The knowledge of the inertia tensor of a solid is of fundamental importance in many branches of applied mathematics, computer science and mechanics. In mechanics the motion of a rigid body is controlled by the inertia tensor of a body through Euler’s equations [1]. If the tetrahedron inertia tensor can be calculated with respect to the same reference system, the inertia tensor for the entire solid can be obtained as the sum of those inertia tensors.
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