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Benjamin Peirce:

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
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Analytical table of contents
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
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
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
Alphabetical index
Figures 1 and figures 2

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