Vector Rotators of Rigid Body Dynamics with Coupled Rotations around Axes without Intersection

Figure 1

Arbitrary position of rigid body coupled rotations around two axes without intersection. System is with two degrees of mobility (two freedom or one degree of freedom and one rheonomic constraint) where 𝜑₁ and 𝜑₂ are generalized coordinates fixed coordinate system and two moveable coordinate systems 𝑂₁𝜉₁𝜂₁𝜁₁=𝑂₁𝜉₁𝜂₁𝑧 and 𝑂₂𝜉₂𝜂₂𝜁₂=𝑂₂𝜉₂𝜂₂𝑧₂ that are rotating with component angular velocities of rigid body coupled rotations: independent generalized (/or rheonomic) coordinates are 𝜑₁ coordinate of precession rotation and 𝜑₂ coordinate around self rotation axis. Vector rotators ℜ₀₁, ℜ₀₁₁, and ℜ₀₂₂ are presented.