Lectures related to Radius of curvature

Explores the theory and applications of helical curves, focusing on circular helices with various parameters.

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Geodesic Curves: Minimizing Distance and Constant Speed

Covers geodesic curves parameterized at constant speed to minimize distances between points.

Introduction to Structural Mechanics

Explores beam bending, stiffness, and curvature in mechanical systems using OCR-extracted slides from EPFL's Spring 2021 session.

Minimal Surfaces and Discrete Differential Geometry

Explores minimal surfaces, curvature, Laplace-Beltrami operator, numerical solutions, Laplacian smoothing, diffusion flow, and time integration.

Weingarten Application of Regular Surfaces

Covers the application of the Weingarten map on regular surfaces and the shape operator.

Nonlinear Beam Theory: Curved Beams Mechanics

Covers the theory of nonlinear curved beams, discussing inextensible strains, finite rotations, and the exact inextensionable theory.

Hyperbolic Geometry

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Structural Mechanics: Beam Bending and Boundary Conditions

Explores the moment-curvature relation for beams, emphasizing stress distribution and typical boundary conditions.

Stresses due to Flexure

Covers the calculation of curvature in beams and the design of beams for stress considerations.

Nonlinear Beam Theory: Mechanics of Slender Structure

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

Concave Mirrors: Focal Length and Reflection Laws

Explores the focal length of concave mirrors and reflection laws.

Differential Geometry: Parametric Curves & Surfaces

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Helix Trajectory and Coordinate Systems

Covers the trajectory and speed of a ball on a helix using cylindrical coordinates.

Normal and Tangential Acceleration

Explores vector acceleration, decomposing it into tangential and normal components related to changes in scalar velocity and the trajectory's curvature.

Altitude Models: Derivative Variables

Covers global relief indicators, altitude models, slope, orientation, curvature, and morphological indices for terrain description.

Plates I: Deformation and Energy

Covers the deformation of plates in pure bending, total strain energy, and wrinkling phenomena, exploring applications and implications of substrate stiffness on wrinkling.

Beams: Forces, Stresses, and Deformations

Analyzes beams, forces, stresses, deformations, curvature, deflection, and rigidity.

Concave Mirrors: Image Formation and Ray Tracing

Explores the focal length-radius relationship, ray tracing for image characteristics, and object placement for concave mirrors.