Geodesic
Kinematic formulas of a rigid body in connection with the modified determination of the final rotation vector
Theoretical and applied mechanics, Tome 10 (1984) no. 1, p. 139
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It is suggested that the position of a rigid body is determined by means of ambiguous parameters (coordinates of a vector), whose dependence on position has no analytical properties (the dependence of a system of three unique parameters must have properties in the form of a coherent topological construction of the multiplicity of the position of a rigid body). This allows Euler's equations of dynamics to be joined by three kinematic relations, thus obtaining a closed system of six differential equations for determining the position of a rigid body as a function of time. 
@article{TAM_1984_10_1_a13,
     author = {Ya. V. Tatarinov},
     title = {Kinematic formulas of a rigid body in connection with the modified determination of the final rotation vector},
     journal = {Theoretical and applied mechanics},
     pages = {139 },
     year = {1984},
     volume = {10},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAM_1984_10_1_a13/}
}
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Ya. V. Tatarinov. Kinematic formulas of a rigid body in connection with the modified determination of the final rotation vector. Theoretical and applied mechanics, Tome 10 (1984) no. 1, p. 139 . http://geodesic.mathdoc.fr/item/TAM_1984_10_1_a13/