Vectors and Tensors: Mathematical Preliminaries and Transformations

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Vector Transformation and Tense

Explores the transformation of vectors and tensors, including rotations and representations in quantum physics.

Chemical Environments: Representations and Correlations

Explores chemical environment representations, symmetrized correlations, and machine learning applications at the atomic scale.

Spherical Tensors and Wigner-Eckart Theorem

Covers the transformation of vectors and tensors in quantum physics.

Deformation and Strain Tensors

Explores deformation and strain tensors, Lagrange representation, elasticity theory, and the divergence theorem.

Deformation Analysis in Solids

Explores the analysis of deformation in solids, emphasizing the importance of understanding stress, rotation, and translation.

Finite & Infinite Deformation: Key Distinction

Explains the geometric interpretation of eigen vectors and values in material deformation.

Nonlinear Beam Theory: Mechanics of Slender Structure

Covers strain-displacement relations, simplifications, constitutive relations, equilibrium equations, and circular rings.

Polar Decomposition Theorem

Explores the Polar Decomposition Theorem, decomposing deformations into stretches and rotations, discussing uniqueness and implications in continuum mechanics.

Deformation Analysis: Small Strain and Kinematics

Explores small strain theory, kinematics, and compatibility conditions in solid mechanics.

Rotations: Angular Momentum

Covers angular momentum in rotations, including preservation of angles and vector products.