Elements of Dynamic: An Introduction to the Study of Motion and Rest in Solid and Fluid Bodies, Volumer 1-3MacMillan and Company, 1878 |
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Side 136
... rolling of one curve on another ; the point of contact being the instantaneous centre . Similar theorems hold good when a body moves about a fixed point , or , which is the same thing , when a spheri- cal surface slides upon an equal ...
... rolling of one curve on another ; the point of contact being the instantaneous centre . Similar theorems hold good when a body moves about a fixed point , or , which is the same thing , when a spheri- cal surface slides upon an equal ...
Side 140
... rolling centrodes , we have 1 1 = - - and s rr = @ 8 - CURVATURE OF ROULETTE . We may derive some important consequences from the expression just obtained for the the acceleration of a point in the moving plane , namely p = ( iw — w3 ) ...
... rolling centrodes , we have 1 1 = - - and s rr = @ 8 - CURVATURE OF ROULETTE . We may derive some important consequences from the expression just obtained for the the acceleration of a point in the moving plane , namely p = ( iw — w3 ) ...
Side 141
... rolling motion . We can now determine the curvature of a roulette at any point . For since the normal acceleration is the squared velocity multiplied by the curvature , we have curvature of path of Ρ • w2 . pc - w ¿ cose w.pc2 = - 1 cos ...
... rolling motion . We can now determine the curvature of a roulette at any point . For since the normal acceleration is the squared velocity multiplied by the curvature , we have curvature of path of Ρ • w2 . pc - w ¿ cose w.pc2 = - 1 cos ...
Side 145
... rolling centrode is a curve in the moving plane which shall be called the curve A. This curve is clearly the envelop of the line of centres in the moving plane . Let us now fix the moving plane , and move the fixed plane , subject to ...
... rolling centrode is a curve in the moving plane which shall be called the curve A. This curve is clearly the envelop of the line of centres in the moving plane . Let us now fix the moving plane , and move the fixed plane , subject to ...
Side 148
... rolling of two equal and similar hyperbolas . For in this case we have απ do : - = ao - bo = ab , so that the locus of o is a hyperbola having a , d for foci and ab for transverse axis . Remarks may be made about the path of a point in ...
... rolling of two equal and similar hyperbolas . For in this case we have απ do : - = ao - bo = ab , so that the locus of o is a hyperbola having a , d for foci and ab for transverse axis . Remarks may be made about the path of a point in ...
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Elements of Dynamic: An Introduction to the Study of Motion and ..., Volum 1 William Kingdon Clifford Uten tilgangsbegrensning - 1878 |
Elements of Dynamic: An Introduction to the Study of Motion and ..., Volum 1 William Kingdon Clifford Uten tilgangsbegrensning - 1878 |
Elements of Dynamic: An Introduction to the Study of Motion and ..., Volumer 1-3 William Kingdon Clifford Uten tilgangsbegrensning - 1878 |
Vanlige uttrykk og setninger
abcd acceleration angular velocity approximately axes axis axode bisects ca² called centimeter centrode circle circulation round complex number component compound conjugate diameters constant cross-ratio curvature curve of positions cycloidal cylinder cylindroid described direction displacement draw eccentric anomalies ellipse ellipsoid equal equation equipotential surface expansion finite fixed point flux function given Hence hodograph homogeneous strain hyperbola hyperboloid instant interval inverse length lines of flow magnitude mean velocity moving plane moving point multiplied orbit parabola parallelogram path perpendicular projection quantity radius rate of change ratio represented resultant right angles rigid body rolling rotation scalar screw shew simple harmonic motion solid angle sphere spin step straight line strained position suppose surfaces of revolution theorem translation triangles twist uniform circular motion vector velocity-potential velocity-system vortex-filament zero
Populære avsnitt
Side 102 - A conic is the locus of a point whose distance from a fixed point called the focus is in a constant ratio to its distance from a fixed line, called the directrix.
Side 99 - E, &c., causing the body to describe in the successive intervals of time the straight lines CD, DE, EF, &c., these will all lie in the same plane ; and the triangle SCD will be equal to the triangle SBC, and SDE to SCD, and SEF to SDE. Therefore equal areas are described in the same...
Side iii - CLIFFORD- THE ELEMENTS OF DYNAMIC. An Introduction to the Study of Motion and Rest in Solid and Fluid Bodies.
Side 98 - ... fixed center of force, are in one fixed plane, and are proportional to the times of describing them. Let the time be divided into equal parts, and in the first interval let the body describe the straight line AB with uniform velocity, being acted on by no force. In the second interval it would, if no force acted, proceed to c in AB produced, describing Be equal to AB : so that the equal areas ASB, BSc described by radii AS, BS, cS drawn to the center S, would be completed in equal intervals.
Side 31 - A, it may be resolved into two components, one in the plane PCA and the other perpendicular to it, and both tangential to the spherical surface.
Side 103 - SP-HP=2a; that is, the difference of the focal distances of any point on the hyperbola is equal to the transverse axis. 219. The equation y* = -i (x2 — a2), may be written y=~. (xHence (see Fig. to Art. 213), _ AM.A'M~ AC*' Tangent and Normal to an Hyperbola.
Side 33 - ... the resultant of any number of simple harmonic motions of the same period and in the same line.