Classical Mechanics by Rajesh Kumar Verma and Pushpendra Kumar Gangwar is a comprehensive and concept-oriented textbook designed strictly according to the FYUGP NEP Physics Major/Minor syllabus of leading Indian universities. This book caters to students of:

• 4th Semester – Gauhati University (GU)

• 5th Semester – Bangalore University (BU)

• 7th Semester – Delhi University (DU)

• Various semesters of AU, RTU, and other autonomous and state universities

Published by Mahaveer Publications, the book provides a strong foundation in classical mechanics, blending mathematical precision with conceptual clarity to support undergraduate physics learning under the NEP curriculum.

Beginning with the fundamental principles of Newtonian mechanics, the book progresses through advanced formulations such as Lagrangian and Hamiltonian dynamics,

UNIT I: NEWTONIAN DYNAMICS

• Newton’s laws, inertial and non-inertial frames

• Momentum & energy techniques

• Mechanics of a system of particles

• Center of mass and Newtonian formulation

• Constraints and generalized coordinates

• Cyclic coordinates and symmetry principles

• Time-translation symmetry and conservation laws

• Integral invariants

• Phase space, flows, and stability theory

• Linear stability, bifurcations

• Integrable vs non-integrable systems

• Introduction to Hamiltonian systems

UNIT II: MOTION IN CENTRAL FORCE SYSTEM

• Motion in central force fields

• Planar motion and angular momentum

• Conservation laws

• Orbital stability

• Inverse-square law and Kepler’s problem

• Bound and unbound orbits

• Scattering and cross-sections

• Harmonic oscillator problem

• Forced oscillations in one dimension

• Damped oscillations

• Systems with many degrees of freedom

• Coupled oscillators, normal modes

• Integrable and chaotic oscillations

• Return maps and area-preserving maps

• Poincaré maps, strange attractors

UNIT III: LAGRANGIAN & HAMILTONIAN FORMALISM

• D’Alembert’s principle & generalized coordinates

• Lagrangian dynamics and transformations

• Configuration space and geometry of motion

• Least action principle, Euler-Lagrange equations

• Symmetry and conservation laws

• Canonical momenta

• Hamiltonian dynamics in phase space

• Canonical transformations

• Poisson brackets & algebraic structure

• Generating functions

• Hamilton-Jacobi equation

• Action-angle variables

• Integrable canonical flows

UNIT IV: TRANSFORMATIONS & RIGID BODY DYNAMICS

• Linear transformations, rotations & rotating frames

• Galilean and similarity transformations

• Dynamics in rotating reference frames

• Coriolis and centrifugal forces

• Rigid body dynamics:

  • Euler angles

  • Angular momentum & kinetic energy

  • Moment of inertia tensor

  • Euler’s equations of motion

• Symmetrical top

• Integrable & non-integrable problems

UNIT V: NON-CANONICAL SYSTEM DYNAMICS

• Non-canonical flows & examples

• Flows on spheres

• Local vs complete integrability

• Global integrability conditions

• Attractors and dynamical stability

• Damped driven Euler–Lagrange dynamics

• Lyapunov exponents

• Geometry & integrability

• Damped Newtonian dynamics

• Period-doubling phenomenon

• Fractal & multifractal orbits

• Strange attractors

• Two-frequency problem

 central force motion, rigid body dynamics, oscillations, and conservation laws. Each chapter is written in a clear, student-friendly manner with definitions, derivations, solved examples, and practice problems aligned with university requirements.