Mathematical Problems in Engineering / 2011 / Article / Fig 3

Research Article

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

Figure 3

Schematic presentation of deviational planes and component directions of the vector rotators of rigid body-disk dynamics with coupled rotation around two orthogonal axes without intersection. (a) Deviation plane containing body mass center 𝐢 , vector of relative mass center position βƒ— 𝜌 𝐢 in relation to the pole 𝑂 2 , and self rotation axis oriented by unit vector  𝑛 2 . (b) Deviation plane containing self rotation axis oriented by unit vector  𝑛 2 and body mass inertia moment vector βƒ— 𝔍 ( 𝑂 2 )  𝑛 2 and its deviational component vector of mass deviational moment βƒ— 𝔇 ( 𝑂 2 )  𝑛 2 for self rotation axis and pole 𝑂 2 . (c) Two deviational planes through pole 𝑂 2 : deviation plane containing self rotation axis oriented by unit vector  𝑛 2 and body mass inertia moment vector βƒ— 𝔍 ( 𝑂 2 )  𝑛 2 and its deviational component vector of mass deviational moment βƒ— 𝔇 ( 𝑂 2 )  𝑛 2 for self rotation axis and pole 𝑂 2 and deviation plane containing axis parallel to fixed axis oriented by unit vector  𝑛 1 and body mass inertia moment vector βƒ— 𝔍 ( 𝑂 2 )  𝑛 1 and its deviational component vector of mass deviational moment βƒ— 𝔇 ( 𝑂 2 )  𝑛 1 for axis oriented by unit vector  𝑛 1 and through pole 𝑂 2 . (d) Schematic presentation of the rigid body-disk skew and eccentrically positioned on the self rotation axis with corresponding mass moment vectors and deviation plane as a detail of the rigid body-disk coupled rotation around two orthogonal axes without intersection.
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