Category: Classical Mechanics

Thornton & Marion, Classical Dynamics (5th Edition) Chapter 1. Matrices, Vectors, and Vector Calculus Problem 19. Vector Algebra The problem asks you to derive Angle transformation formulae using vector algebra. You should know about Basic concept of a vector algebra Law of cosines Pythagorean trigonometric identity Solution (a)   From the law of cosines, (b)…

Thornton & Marion, Classical Dynamics, Fifth Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 18. Geometrical interpretation of the vector product Solution

Thornton & Marion, Classical Dynamics, Fifth Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 17. Geometrical interpretation of the scalar product Solution

Thornton & Marion, Classical Dynamics, Fifth Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 16. Geometrical interpretation of the scalar product Solution

Thornton & Marion, Classical Dynamics, Fifth Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 15. Orthogonal matrix Solution

Thornton & Marion, Classical Dynamics, Fifth Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 14. Vector calculus Solution

Thornton & Marion, Classical Dynamics, Fifth Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 13. Vector triple product (BAC-CAB rule) Solution

Thornton & Marion, Classical Dynamics, Fifth Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 12. Application of the scalar and vector product (Geometrical interpretations) Solution  

Thornton & Marion, Classical Dynamics, Fifth Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 11. Triple scalar product The problem asks you to show that 1) triple scalar product can be written as 2) the product is unaffected by an interchange of operators or by a change in the order. 3) a geometrical interpretation,…

Thornton & Marion, Classical Dynamics, Fifth Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 10. Differentiation of a vector The problem asks you to calculate vector derivatives to get velocity and acceleration of a particle. The problem gives position vector of a particle in a plain elliptical orbit. We should know about calculation of…