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Hamilton’s Principle for0:00:15

Hamilton’s Principle for Field Lagrangians

Field Lagrangians0:00:15

Field Lagrangians

The Reduced Phase0:00:15

The Reduced Phase Space

Liouville’s Theorem0:00:15

Liouville’s Theorem

Small Oscillations (Simple0:00:15

Small Oscillations (Simple Harmonic Motion)

The Hamiltonian Flow0:00:15

The Hamiltonian Flow

Stationary Values0:00:15

Stationary Values

Hamilton’s Principle0:00:15

Hamilton’s Principle

The Cotangent Bundle0:00:15

The Cotangent Bundle of Configuration Space (Phase Space)

The Configuration Space0:00:15

The Configuration Space of: Chassis, Reaction Wheel and Rolling Wheel

Braking with a0:00:41

Braking with a Brushless Motor

Linear Measurement of0:00:48

Linear Measurement of a Tetrahedron

Stretch with Multiplication0:00:15

Stretch with Multiplication by a Real Number

How to Stretch0:00:15

How to Stretch the Fiber Space with Multiplication by a Complex Number

A Local Path0:00:15

A Local Path Dependence with Bundle Curvature

How to Make0:00:15

How to Make a Curved Connection on a Fiber Bundle

Types of Connection0:00:15

Types of Connection on ℝ² Compared

Connection on a0:00:15

Connection on a Strained Plane Bundle

The Tangent and0:00:15

The Tangent and Cotangent Bundles of S³

A Complex Line0:00:15

A Complex Line Bundle

The Tangent Bundle0:00:15

The Tangent Bundle to the Sphere and The Clifford Bundle

The Total Space0:00:15

The Total Space of the Clifford Bundle

A Cross-Section of0:00:15

A Cross-Section of a Fiber Bundle

The Zero Section0:00:15

The Zero Section of A Vector Bundle