Category: Classical Mechanics

Thornton & Marion, Classical Dynamics (5th Edition) Chapter 1. Matrices, Vectors, and Vector Calculus Problem 21. Triple scalar product and Levi-Civita symbol The problem asks you to show  The relation between the triple scalar product and Levi-Civita Symbol You should know about Vector and scalar product Triple scalar product (Problem 1-11) Definition of Levi-Civita symbol…

Thornton & Marion, Classical Dynamics (5th Edition) Chapter 1. Matrices, Vectors, and Vector Calculus Problem 20. Kronecker delta & Levi-Civita Symbol The problem asks you to prove Some properties of Kronecker delta and Levi-Civita Symbol You should know about Definition of Kronecker delta symbol (Equation 1.14) Definition of Levi-Civita symbol (Equation 1.67) Solution References https://en.wikipedia.org/wiki/Kronecker_delta…

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 The basic concept of a vector algebra Law of cosines Pythagorean trigonometric identity Solution References https://en.wikipedia.org/wiki/Law_of_cosines https://en.wikipedia.org/wiki/Pythagorean_trigonometric_identity

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