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.
Highlights
The motion in a non-inertial reference frame and in electric and magnetic fields are important tools, both in theoretical problems and practical applications
Even though the problems discussed in the paper can be found in classical mechanics textbooks [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20], they were never solved in all their general aspects
The symbolic tensor instrument presented in this paper simplifies the complex initial value problem that models the motion in a non-inertial reference frame, and was introduced in Reference [21]
Summary
The motion in a non-inertial reference frame and in electric and magnetic fields are important tools, both in theoretical problems and practical applications. The motion of a mass particle in a uniform gravitational field in a rotating reference frame, the motion of a charged particle in non-stationary electric and magnetic fields, and the exact solution of the relative rigid body motion in a non-inertial reference frame are studied. Using these mathematical results, in the fourth and fifth section, we analyze the motion of a mass particle in a uniform gravitational field with respect to a non-inertial reference frame and the motion of a charged particle in non-stationary electric and magnetic fields, respectively. The motion of a rigid body with respect to a non-inertial reference frame is studied, and an exact closed-form solution is given for this motion.
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