Lectures related to Generalized Forces: Modeling and Examples

Virtual Work in Structural Mechanics

Explores virtual work in structural mechanics, emphasizing equilibrium states and the application of virtual displacements.

Molecular dynamics under constraints

Explores molecular dynamics simulations under holonomic constraints, focusing on numerical integration and algorithm formulation.

Lagrange's Approach: Dynamics and Constraints

Explores Lagrange's approach to dynamics, emphasizing compatibility with constraints and the significance of generalized coordinates.

Constraints and Lagrange

Introduces constraints, Lagrange multipliers, and generalized coordinates in physics.

Structural Mechanics Principles: Equilibrium and Stability

Explores the principles of structural mechanics, including internal loads, equilibrium stability, and the superposition principle.

Virtual Work II: Examples of Potentials

Covers examples of potentials in virtual work for structural mechanics.

Virtual Work Principles: Energy and Mechanics

Covers work, potential energy, and the principle of virtual work in structural mechanics.

Principle of Least Action

Covers the principle of least action, Euler-Lagrange equations, Lagrange multipliers, and variational calculus.

Lagrange I: Conservation Laws and Kinetic Energy

Explores Lagrangian mechanics, conservation laws, and kinetic energy in generalized coordinates.

Virtual Work II

Explores virtual work in mechanical systems, equilibrium of external loads, and linear elastic behavior in beams.

Introduction to Structural Mechanics

Introduces structural mechanics concepts like distributed loads, centroids, and equilibrium in 2D and 3D.

Lagrange II: Principle of D'Alembert

Explores the Principle of D'Alembert and perfect constraints in mechanical systems, demonstrating their application through examples like the simple pendulum.

Virtual Work I: Introduction to Structural Mechanics

Introduces work, potential energy, and virtual work in structural mechanics, emphasizing equilibrium conditions and their application to solve problems.

Mechanics: Equilibrium Points and Stability

Explores equilibrium points and stability in mechanical systems, analyzing how systems return to or move away from their positions after disturbances.

Systems of Forces in 3D

Explores systems of forces in three dimensions, emphasizing moments and couples, equilibrium, and scalar components.

Lines of Influence: Theorem of Virtual Displacements

Explores lines of influence, emphasizing finding unfavorable load positions and drawing support reaction lines without calculations.

Solid Identification: Coordinates and Orientation

Covers the identification of a solid in space using 6 coordinates and the concept of undeformable solid bodies.

Variational Calculus and Least Action Principle

Covers the principle of least action and variational calculus in discovering equations of motion.

Analytical Mechanics: Lagrange Formalism

Covers the limitations of Lagrange formalism and the transition to Hamiltonian formalism for dynamic variables.

Equilibrium and Forces in 3D: Structural Mechanics

Covers resultants in 3D and equilibrium principles in structural mechanics.