We know velocity is a parameter defining dynamics; however, inertia is a property that defines statics. From mathematical physics point of view, is it possible to analyze velocity and the inertia in the platform of matrix space metrics?
there is no dynamical variable termed inertia.
Inertia is the property by which a body remains at rest or in constant rectilinear motion unless acted on by forces.
You may be asking if position and linear momentum along the same direction are conjugate dynamical variables. The answer is yes, but this is only significant when you
study modern physics.
Linear momentum is mv, v is velocity vector along some direction, m is mass.
the term metric is inapropriate in this context. It refers to a geometric concept of distance mesurement.
Moments of inertia are precisely defined as dynamic variables and may be found in matrix operations with other variables.
OK, you mean the moment of inertia tensor. It has just to do with geometry and the mass of the object, not dynamical.
It connects angular momentum vector with rotation frequency vector. The later two
can be termed dynamical.
Maybe thats why Rayan termed it statics.
I cannot see any direct connection between that and velocity.
Velocity and inertia are not directly connected.
According to Newton's first law, inertia is defined as the "resistance" of a massive body to its state of motion being changed by an external force, so inertia is resistance to "change-of-state-of-motion".
This is true whether or not a massive body is in motion (velocity involved) or not (velocity not involved).
If not moving, it will resist being set in motion. when in motion it will resist having its velocity slowed down or increased and it will resist its straight line trajectory being changed even when its velocity is maintained.
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