Group 1: Branches of Classical Mechanics
– Statics: Analyzes force and torque on systems in equilibrium.
– Kinematics: Studies motion without considering forces; seen as the geometry of motion.
– Dynamics: Considers forces explaining object behavior; some authors include special relativity in classical dynamics.
Group 2: Mathematical Formalisms in Classical Mechanics
– Newtonian Mechanics: Emphasizes force as a vector quantity; equations of motion derived from Newton’s Second Law.
– Analytical Mechanics: Uses scalar properties like kinetic and potential energy; includes Lagrangian and Hamiltonian mechanics.
– Principle of Least Action: Equations of motion can be derived from this principle.
Group 3: Application Areas of Classical Mechanics
– Celestial Mechanics: Deals with celestial bodies like stars and planets.
– Continuum Mechanics: Models materials as a continuum.
– Relativistic Mechanics: Includes special and general theories of relativity.
– Statistical Mechanics: Relates microscopic properties to macroscopic properties.
Group 4: Key Concepts in Classical Mechanics
– Objects and Motion: Analysis of projectile motion; use of point particles to model objects.
– Laws and Principles: Newton’s laws, Euler’s laws, and assumptions about matter and energy.
– Frames of Reference: Inertial frames, non-inertial frames, and introduction of fictitious forces.
– Special Relativity: Concepts related to time, space, and inertial frames in classical mechanics.
Group 5: Advanced Topics and Limits of Classical Mechanics
– Work and Energy: Definition of work, kinetic energy, and the work-energy theorem.
– Hamiltonian Mechanics: Formulation, equations, and its link to classical and quantum mechanics.
– Limits of Validity: Comparison with more accurate theories like general relativity and quantum field theory.
– Approximations: Newtonian approximation to special relativity and classical approximation to quantum mechanics.
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Classical mechanics is a physical theory describing the motion of objects such as projectiles, parts of machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics involved substantial change in the methods and philosophy of physics. The qualifier classical distinguishes this type of mechanics from physics developed after the revolutions in physics of the early 20th century, all of which revealed limitations in classical mechanics.
The earliest formulation of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on the 17th century foundational works of Sir Isaac Newton, and the mathematical methods invented by Gottfried Wilhelm Leibniz, Leonhard Euler and others to describe the motion of bodies under the influence of forces. Later, methods based on energy were developed by Euler, Joseph-Louis Lagrange, William Rowan Hamilton and others, leading to the development of analytical mechanics (which includes Lagrangian mechanics and Hamiltonian mechanics). These advances, made predominantly in the 18th and 19th centuries, extended beyond earlier works; they are, with some modification, used in all areas of modern physics.
If the present state of an object that obeys the laws of classical mechanics is known, it is possible to determine how it will move in the future, and how it has moved in the past. Chaos theory shows that the long term predictions of classical mechanics are not reliable. Classical mechanics provides accurate results when studying objects that are not extremely massive and have speeds not approaching the speed of light. With objects about the size of an atom's diameter, it becomes necessary to use quantum mechanics. To describe velocities approaching the speed of light, special relativity is needed. In cases where objects become extremely massive, general relativity becomes applicable. Some modern sources include relativistic mechanics in classical physics, as representing the field in its most developed and accurate form.
