Hamilton’s Equations Explained: Pendulum Constrained to a Parabola

Описание: In this video, we dive into the elegant framework of Hamiltonian mechanics to analyze a simple pendulum constrained to move along a parabolic path. Using the principles of analytical mechanics, we derive the Hamiltonian, obtain the canonical equations of motion, and explore how the system evolves over time.

This is a perfect example of how constraints shape the dynamics of a system, and how Hamilton’s formulation offers a powerful alternative to Newtonian and Lagrangian mechanics.

🔍 What You’ll Learn:
How to model a constrained system using Hamiltonian mechanics

Derivation of the Hamiltonian for a pendulum on a parabola

Interpretation of generalized coordinates and momenta

Canonical equations of motion and their physical meaning

Phase space perspective of the motion

📘 Level: Advanced (Classical Mechanics / Analytical Mechanics)
📈 Ideal for: University students, educators, physics enthusiasts

🏷️ Keywords / Palabras clave
Hamiltonian mechanics

Constrained motion

Analytical mechanics

Canonical equations

Phase space

Parabolic constraint

Simple pendulum physics

Advanced classical mechanics

Física analítica

Ecuaciones canónicas

Mecánica clásica avanzada

Péndulo en parábola

Movimiento con restricciones

Energía y dinámica

🔖 Hashtags
English:
#HamiltonianMechanics #ClassicalMechanics #AnalyticalMechanics #PhysicsLecture #ConstrainedSystems #PhaseSpace #PhysicsAnimation

Spanish:
#MecánicaHamiltoniana #FísicaClásica #EcuacionesDeHamilton #SistemaRestringido #EspacioFase #Péndulo #FísicaAvanzada