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Thornton & Marion, Classical Dynamics, 5th Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 12. Application of the scalar and vector product (Geometrical interpretations) 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, 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, Classical Dynamics, 5th Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 09. Vector calculation The problem asks you to evaluate some vector calculations. The problem gives We should know about Addition and subtraction of vectors Dot product and cross product of vectors Solution
Thornton & Marion, Classical Dynamics, 5th Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 08. An equation of a plane in vector form The problem asks you to Show that the given equation is the equation of a plane. This problem assumes be a vector from the origin to a fixed point be a…
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, 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, 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…
Thornton & Marion, Classical Dynamics, 5th Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 04. Transposed and Inverse Matrix The problem asks you to prove the properties of the transposed and inverse matrix. You should know about Transposed matrix Inverse matrix Solution (a) Let , then By definition of transpose, Therefore, (b) i) For…
Thornton & Marion, Classical Dynamics, 5th Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 03. Transformation Matrix The problem asks you to find a transformation matrix that satisfying some conditions. This problem gives (or assumes) This matrix rotates a rectangular coordinate through an angle of 120 degrees about an axis making equal angles with…