Thornton & Marion (5th Edition), Chapter 01, Problem 11 Solution

Thornton & Marion, Classical Dynamics, 5th Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 11. Triple scalar product The problem asks you to Triple scalar product can be written as The product is unaffected by an interchange of operators or by a change in the order. A geometrical interpretation, which is the volume of…

Thornton & Marion (5th Edition), Chapter 01, Problem 10 Solution

Thornton & Marion, Classical Dynamics, 5th Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 10. Differentiation of a vector The problem asks you to calculate vector derivatives to get the velocity and acceleration of a particle. The problem gives position vector of a particle in a plain elliptical orbit. We should know about calculation…

Thornton & Marion (5th Edition), Chapter 01, Problem 07 Solution

Thornton & Marion, Classical Dynamics, 5th Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 07. Scalar Product of two (unit) vectors The problem asks you to Find the vectors describing the diagonals The angle between diagonal vectors This problem assumes A unit cube in the Cartesian (Rectangular) coordinate system We should know about Position…

Thornton & Marion (5th Edition), Chapter 01, Problem 06 Solution

Thornton & Marion, Classical Dynamics, 5th Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 06. Another proof of the orthogonality condition The problem asks you to prove that Equation (1.15) can be obtained by using the fact that the transformation matrix preserves the length of the line segment. This problem assumes that the coordinate…

Thornton & Marion (5th Edition), Chapter 01, Problem 05 Solution

Thornton & Marion, Classical Dynamics, 5th Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 05. The determinant of the transformation matrix The problem asks you to show that This problem assumes The transformation matrix to be a two-dimensional orthogonal matrix. You should know about Calculation of a determinant Properties of the orthogonal transformation matrix…