EXPONENTIAL SOLUTION OF A DIFFERENTIAL EQUATION BETWEEN OPERATORS
In this paper we obtain an authentically exponential
solution to the differential equation dY (t)/ dt = A(t)Y (t), where Y (t) and A(t)
are linear operators with the initial condition Y (0) = I, and I is the identity
operator. Then, the solution was applied to calculate the vector triad: tangent,
normal and binormal in terms of the arc length of a curve.
Keywords:
Exponential of a matrix Lie groups, Frenet-Serret equation,
___
- [1] J. Schwinger, Phys. Rev. 74 (1948),1439-1461.
- [2] F. J. Dyson, Phys. Rev. 75 (1949), 486-502.
- [3] R. P. Feynman, J. Phys. Rev. 84 (1951),108-128.
- [4] H. Luna-Garcia, O. Chavoya-Aceves, Rev. Mex. Fis. 35(4) (1980),680-690.
- [5] W. Magnus, Comm. Pure Appl. Math., Vol. VII, (1954),649-673.
- [6] Abramowitz and Stegun, Handbook of Mathematical Functions, Dover Publications,USA (1964).
- [7] R. M. Wilcox, J. Math. Phys. 8 (1967),962-982.
- [8] B. Mielnik, J. Pleba˜nski, Ann. Inst. Henri Poincar´e, Vol. XII, No. 3, (1970), 215-254.
- [9] E. B. Dynkin, Doclady Akad. Nauk, SSSR (N. S.) 57(1947), 323-326.
- [10] K. O. Friederich, Comm. Pure Appl. Math., Vol. VI, (1953),1-72.
- [11] D. Danielson, Vectors and Tensors in Engineering and Physics, 2nd. Ed., Addison-Wesley,USA (1992).
- [12] H. Goldstein. Classical Mechanics, 2nd. Ed., Addison-Wesley,USA (2000).
- ISSN: 2147-6268
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 2013
- Yayıncı: -