Treatise on Natural PhilosophyThis work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. |
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Contents
PRELIMINARY | 1 |
Displacements of a Plane Figure in its PlaneComposition | 78 |
Most general Motion of a Rigid Body 102 | 102 |
Free rotation of a Body kinetically symmetrical about an axis | 108 |
Flexible and Inextensible SurfaceFlexure of inextensible | 114 |
TwistEstimation of Integral Twist in a Plane Curve | 119 |
Surface rolling on Surface without spinning | 125 |
Displacement of a Body rigid or not one point of which | 127 |
Momental EllipsoidEquilibration of Centrifugal Forces | 264 |
Deduction of the Equations of Motion of any SystemInde | 271 |
Moment of an Impact about an AxisBallistic Pendulum | 282 |
General Theorem of Fundamental Modes of infinitely small | 338 |
Kinetics of a perfect fluidEffect of a Rigid Plane on | 340 |
Characteristic FunctionCharacteristic Equation of Motion | 354 |
Slightly disturbed EquilibriumSimultaneous Transformation | 362 |
Case of Equality among PeriodsGraphic Representation | 366 |
Integral CurvatureCurvatura integraHorographChange | 136 |
Equation of ContinuityIntegral Equation of Continuity | 148 |
Freedom and ConstraintOf a PointOf a Rigid BodyGeo | 154 |
APPENDIX A Expression in Generalized Coordinates for Poissons | 160 |
APPENDIX A Extension of Greens Theorem | 167 |
DYNAMICAL LAWS AND PRINCIPLES | 219 |
Resolution of ForcesEffective Component of a Force | 231 |
Virtual VelocityVirtual Moment | 250 |
Conservation of Energy | 251 |
Infinitely small Motion of a Dissipative SystemCycloidal | 384 |
Artificial or Ideal Accumulative SystemCriterion of Sta | 392 |
Kinetic StabilityConservative disturbance of motionKi | 428 |
EXPERIENCE | 440 |
MEASURES AND INSTRUMENTS | 457 |
L | 463 |
APPENDIX B CONTINUOUS CALCULATING MACHINES | 479 |
Mechanical Integration of the general Linear Differential Equation | 500 |
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Common terms and phrases
acceleration action altered angular velocity anticlastic application arbitrary axis Cambridge centre of inertia circle co-ordinates coefficients component condition configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dx dy dy dy dy dz ellipse ellipsoid elongation equal equations of motion equilibrium expression finite fixed force formula function geometrical given gyrostatic Hence impulse infinitely small initial instant integral kinetic energy Lagrange's length linear mass momentum moving P₁ parallel particle path perpendicular polygon position principal axes quadratic quadratic function quantity radius ratio rectangular resultant right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values whole Y₁ αξ аф