The Quarterly Journal of Pure and Applied Mathematics, Volum 11J.W. Parker, 1871 |
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Resultat 1-5 av 43
Side 38
... normal , and therefore v2 = Fp . The velocity at the apse is therefore the velocity which is requisite for circular motion about the centre of force , and the question naturally arises ; " If the particle be projected from the apse with ...
... normal , and therefore v2 = Fp . The velocity at the apse is therefore the velocity which is requisite for circular motion about the centre of force , and the question naturally arises ; " If the particle be projected from the apse with ...
Side 39
... normals dividing the curve symmetrically , and between the curve , and the corresponding vertex of the evolute . If the centre of force lie in any other position , the curve cannot be described , unless it be conceived that the law of ...
... normals dividing the curve symmetrically , and between the curve , and the corresponding vertex of the evolute . If the centre of force lie in any other position , the curve cannot be described , unless it be conceived that the law of ...
Side 40
... normal is the instantaneous centre , and if TP = x , TQ = y , x and y are the coordinates of the carried locus of E , and since and OY = p = f ( $ ) , dp PY = = ƒ ' ( $ ) , аф TY = f ( $ + ) and QY ' = ƒ ' ( † + - ) · Hence the first ...
... normal is the instantaneous centre , and if TP = x , TQ = y , x and y are the coordinates of the carried locus of E , and since and OY = p = f ( $ ) , dp PY = = ƒ ' ( $ ) , аф TY = f ( $ + ) and QY ' = ƒ ' ( † + - ) · Hence the first ...
Side 41
... normals QP , Q'P ' will meet at a point E on the cir- cumference of the fixed circle . It will be easily seen that the line TE passes through 0 , and is four times the radius ( c ) of the rolling circle , so that while the fixed locus ...
... normals QP , Q'P ' will meet at a point E on the cir- cumference of the fixed circle . It will be easily seen that the line TE passes through 0 , and is four times the radius ( c ) of the rolling circle , so that while the fixed locus ...
Side 52
... normal to the area a ,, the elements ds , and the directrix all lie in the plane perpen- dicular to the direction of the force , it follows that , if & be the inclination of the element to the directrix , and 8 be the projection of OP'Q ...
... normal to the area a ,, the elements ds , and the directrix all lie in the plane perpen- dicular to the direction of the force , it follows that , if & be the inclination of the element to the directrix , and 8 be the projection of OP'Q ...
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The Quarterly Journal of Pure and Applied Mathematics, Volum 6 James Joseph Sylvester,James Whitbread Lee Glaisher Uten tilgangsbegrensning - 1864 |
Vanlige uttrykk og setninger
a+b+c action af-g angle angular velocities axes body Cayley centre circle coefficient columns common tangent concyclic cone confocal conic conicoids conjugate coordinates corresponding cubic curvature cusps denote differential dt dt elements ellipsoid envelope equal equation Euler's equations evectant evolute expression fixed point formulæ given curve greatest value Hence inflexion instantaneous axis integral intersection line IJ log mv magic square nodal normal obtain pairs parallel curve perpendicular points of contact pole quadric quartic surface radius reciprocal respectively shewn solenoid solution stationary tangent suppose tangent planes theorem torse triads unlike signs vertex w₁ whence WILLIAM WALTON zero square
Populære avsnitt
Side 187 - On the small oscillations of a Rigid Body about a Fixed Point under the action of any Forces, and more particularly when gravity is the only force acting," Transactions of the Boyal Irish Academy, vol.
Side 59 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 188 - ... to these directions are at right angles. III. A Free Rigid Body. 4. A free rigid body may receive any displacement by being screwed along an axis in space, the distance it travels along the axis when turned through the unit of angle being termed the pitch of the screw.
Side 50 - Д0 be the area of the triangle formed by joining the points of contact of the...
Side 189 - ... of these axes, as about a fixed axis, and its motion is always compounded of vibrations about these axes. 15. The length of the simple pendulum isochronous with the vibration about each normal axis is proportional to the square of the ratio of the corresponding diameter in the ellipsoid of equal energy to that of the momental ellipsoid.
Side 6 - I)2 = 0 ; and by reason of this property it is very easy to find the equations of the reciprocal surfaces, or plane-equations of the quartic surfaces in question. And, in the same paper, it is noticed that the surfaces of the form in question include the reciprocals of several interesting surfaces of the orders 6, 8, 9, 10, and 12 ; viz., order 6, parabolic ring : order 8, elliptic ring : order 9, centrosurface of paraboloid : order 10, parallel surface of paraboloid ; envelope of planes through...
Side 189 - A body rotating about a fixed point has throe degrees of freedom; its motion is compounded of vibrations about three normal screws whose pitch is zero, and whose directions pass through the point. NB — The screws in this case may be conveniently called the normal axes. V.
Side 9 - General Solution and Extension of the Problem of the 15 School Girls,
Side 309 - On the summation by definite integrals of geometrical series of the second and higher orders.