AM 305 (A) CLASSICAL MECHANICS (IE) (Common with paper MA 305 of Branch I(A) Mathematics) UNIT : –I Principle and Some Definitions-Classification of D’Alembert’s Lagrange’s Equations: Dynamical System-Some Examples of Constraints Virtual Displacement-Principle of Virtual Work Force in Holonomic System-Mathematical Expression for –Generalised the principle of Virtual work-D Equations for a Alembert’s principle-Lagrange’s Holonomic system-Velocity-dependent potential Equations of Motion –Lagrange’s for conservative , Non-holonomic system-physcial Significance of 1 –Harmonic Oscillator. UNIT II: – Variational Principle and Variational Principle-Calculus of Lagrange’s Equations: Variations-Hamilton Principle-Derivation of Hamilton’s Principle from Lagrange’s Equations-Derivation of Equations from Principle Lagrange’s Hamilton’s –Extension of Principle Principle for Non-conservative, Non-holonomic Hamilton’s –Hamilton’s System Force in Dynamic system-Hamilton Principle for –Generlised holonomic System -Lagrange’s Equations for Non –conservative –Holonomic System or ignorable Coordinates Theorem-Conservation of –Cyclic –Conservation Linear Momentum in Lagrangian Formulation-Conservation of Angular Momentum in Lagrangian Formulation of Angular Momentum of –Conservation –Conservation Energy in Lagrangian Formulation. UNIT III: – Equations of Motion: Derivation of Equations of Motion Hamilton’s Hamilton’s (using Equations)-Routh’s of Motion-Derivation of Lagrange’s Procedure-Equations Equations from Principle of Least Hamilton’s Hamilton’s –Principle between Principle and Principle of Least Action. Hamilton’s
AM 305 (A) CLASSICAL MECHANICS (IE) (Common with paper MA 305 of Branch I(A) Mathematics) UNIT –I : D’Alembert’s Principle and Lagrange’s Equations: Some Definitions-Classification of Dynamical System-Some Examples of Constraints Virtual Displacement-Principle of Virtual Work –Generalised Force in Holonomic System-Mathematical Expression for the principle of Virtual work-D Alembert’s principle-Lagrange’s Equations for a Holonomic system-Velocity-dependent potential –Lagrange’s Equations of Motion for conservative , Non-holonomic system-physcial Significance of 1 –Harmonic Oscillator. UNIT – II: Variational Principle and Lagrange’s Equations: Variational Principle-Calculus of Variations-Hamilton Principle-Derivation of Hamilton’s Principle from Lagrange’s Equations-Derivation of Lagrange’s Equations from Hamilton’s Principle –Extension of Hamilton’s Principle –Hamilton’s Principle for Non-conservative, Non-holonomic System –Generlised Force in Dynamic system-Hamilton Principle for holonomic System -Lagrange’s Equations for Non –conservative –Holonomic System –Cyclic or ignorable Coordinates –Conservation Theorem-Conservation of Linear Momentum in Lagrangian Formulation-Conservation of Angular Momentum in Lagrangian Formulation –Conservation of Angular Momentum –Conservation of Energy in Lagrangian Formulation. UNIT – III: Hamilton’s Equations of Motion: Derivation of Hamilton’s Equations of Motion (using Lagrange’s Equations)-Routh’s Procedure-Equations of Motion-Derivation of Hamilton’s Equations from Hamilton’s Principle –Principle of Least between Hamilton’s Principle and Principle of Least Action.