1. Exact Closed-Form Solutions of the Motion in Non-Inertial Reference Frames, Using the Properties of Lie Groups SO3 and SE3
- Author
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Eugen Șfartz and Daniel Condurache
- Subjects
Inertial frame of reference ,Physics and Astronomy (miscellaneous) ,electric and magnetic fields ,General Mathematics ,rigid body motion ,Mathematical analysis ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,closed-form exact solution ,Lie group ,Rotating reference frame ,Rigid body ,Motion (physics) ,Analytical mechanics ,Chemistry (miscellaneous) ,Computer Science (miscellaneous) ,QA1-939 ,Lie groups SO3 and SE3 ,Non-inertial reference frame ,Mathematics ,non-inertial reference frame ,Poisson-Darboux problem ,Reference frame - Abstract
The paper offers a general symbolic method to study the motion in a non-inertial reference frame. In order to achieve this, we use the algebraic and geometric properties of the Lie group of special orthogonal tensors, SO3, and the Lie group of the rigid body displacements, SE3. We obtain a simplified form of the initial value problem that models the non-inertial motion using a tensor instrument introduced in this paper. Thus, the study of the motion in a non-inertial reference frame is transferred into the study of a classical motion in an inertial reference frame. The applications of this method refer to solving the relative motion problem and deriving the straightforward solution to classical theoretical mechanics problems. The motion in a uniform gravitational force field in a rotating reference frame, the motion of a charged particle in non-stationary electric and magnetic fields, the exact solution of the relative rigid body motion in the non-inertial reference frame are studied. Using this symbolic method in studying the motion in a non-inertial reference frame reduces the number of computations. In addition, it offers, in some essential particular cases, exact closed-form coordinate-free analytical solutions.
- Published
- 2021
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