## A system of Analytic Mechanics

#### Boston, Little, Brown and Company, 1855

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 Handwritten note of the author: This copy of Analytic Mechanics is deposited in the Library of Harvard College to be used by special students with the approbation in writing. The professor of Mathematics - Benjamin Peirce
 Physical and Celestial Mechanics, by Benjamin Peirce, Boston, Little, Brown and Company, 1855
 A system of Analytic Mechanics, by Benjamin Peirce, Boston, Little, Brown and Company, 1855
 Harvard College Library, March 25, 1870, Gift of the author
 To the cherished and revered memory of my master in Science, Nathaniel Bowditch, The father of American Geometry, this volume is inscribed
 Advertisement: Originally prepaired as part of a course of lectures for the students of mathematics at Harvard College...
 List of subscribers
 Chapter I: Motion, Force and Matter
 Chapter II: Measure of Motion and Force
 velocity, power, mass, v = DsP.
 Newtons law m Dt v = F
 Chapter III: Fundamental principles of rest and motion
 Lagrange description of mechanics
 Chapter IV: Elements of motion. Motion of translation
 Translation and rotation
 Rotation, axes of rotation
 Combined motion of rotation and translation
 Couple of rotations of Poinsot, ridid motion (Chasles theorem)
 Special elements of motion and equation of condition
 Method of Lagrange multipliers
 Chapter V: Forces of Nature
 Equilibrium in a potential
 On perpetuum motion machines
 Level surface
 Composition and resolution of forces, projection
 Resultant force
 Moment of inertia
 Angular momentum and Moment of inertia
 Gravitation and the force of statical electricity
 Laplace operator
 Laplace equation
 Attraction between two planes (lamina)
 Poisson equation
 Attraction of an infinite cylinder
 Description using comlex numbers
 Attraction of a finite point upon a distant mass
 Attracton of a surface of finite extent, Chaslesian shells
 Gauss theorem (for gravitation)
 No minima for gravitational potential (maximum principle)
 Chasles theorem: a surface which is levelsurface to its own gravity is Chaslesian shell
 Attraction of ellipsoid
 Potential of ellipsoid. Examples of Chaslesian shells
 Each normal to ellipsoid is intersection of two hyperboloids with same foci
 Attraction of a spheroid
 Legendre functions
 Elasticity
 Chapter VI: Equilibrium of translation
 Chapter VII: Equilibrium of rotation
 Chapter VIII: Equilibrium of equal and parallel forces
 The funicular and the Catenary
 Case of surface of revolution: constant of motion
 Chapter IX: Action of moving bodies
 Principle of living forces or law of power (Lagrange equations)
 Maupertius principle of least action
 Hamilton the principal function (action funtional)
 PDE's for the determination of the characteristic, principal and other functions of the same class
 Chapter X: Integration of the differential equations of motion
 Determinants and functional determinants
 Partial determinants and complete determinants, (Laplace expansion)
 Solutions of linear algebraic equations using determinants
 Functional determinants (Jacobian or determinants of Jacobian matrices)
 Obtaining the determinant by Gaussian elimination
 Multiple derivatives and integrals
 Simultaneous differential equations and linear PDE's of the first order
 Integrals and solutions
 The Jacobian multiplier of differential equations
 Principle fo the last multiplier
 Integrals of the differential equations of motion
 The application of Jacobi's principle of the last multiplier to Lagranges canonical forms
 Chapter XI: Motion of translation
 Motion of a point
 A point moving upon a fixed line
 The motion of a body upon a line, when there is no external force
 Motion of a heavy body upon a fixed line. The simple pendulum
 Motion of a body upon a line in opposition to friction, or through a resisting medium
 Logarithmic spiral
 A point moving upon a fixed surface
 A simple pendulum in a resisting medium
 Comparison of Newtons experiments upon vibrations of the pendulum with computation
 Comparison of Dubuats experiments upon the diminution of the arc of vibration of a pendulum with computation
 Comparison of Borda's observations upon the diminished vibrations of the pendulum with computation
 Bessels experiments
 Comparison of Bessels observed arcs of vibration of the pendulum with the computed arcs
 Experiments with the full cylinder and short suspension
 Bailys experiments
 The tautochrone
 The brachistochrone
 Brachistochrone is cycloid
 The tachytrope
 The barytrope and the tautobaryd
 The synchrone
 The spherical pendulum
 Motion ofa free point
 Chapter XII: Motion of rotation
 Rotation of a solid body
 Rotation of a solid body which is subject to no external action
 Gyroscope
 Rotary progression, nutation and variation
 Roling and sliding motion, the hoop
 Chapter XIII: motion of systems
 Lagranges method of perturbations
 Hansens method of perturbations
 Stability and eigenvalues
 A system moving in a resisting medium
 Appendix A: On the force of moving bodies
 Appendix B: On the theory of orthographic projections
 Errata
 Alphabetical index
 Figures 1 and figures 2

 Last update: 8/5/2004. Back to the department history page