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a particle p of mass 3m is suspended fron a fixed point o by a light linear spring with strength alpha a second
a particle of mass m moves under the central fieldf -m gammae-isinrar2rwhere gamma a and isin are positive constants
solar oblateness a planet of mass m moves in the equatorial plane of a star that is a uniform oblate spheroid the
suppose the solar system is embedded in a dust cloud of uniform density rhofind an approximation to the lsquoannual
orbits in general relativity in the theory of general relativity the path equation for a planet moving in the
1 a uniform flux of particles is incident upon a fixed hard sphere of radius a the particles that strike the sphere are
a uniform flux of particles each of mass m and speed v is incident upon a fixed scatterer that exerts the repulsive
a spacecraft is orbiting the earth in a circular orbit of radius c when the motors are fired so as to multiply the
a body moving in an inverse square attractive field traverses an elliptical orbit with major axis 2a show that the time
a body moving in an inverse square attractive field traverses an elliptical orbit with eccentricity e and major axis 2a
a spacecraft is lsquoparked in a circular orbit 200 km above the earths surface the spacecraft is to be sent to the
a spacecraft is lsquoparked in an elliptic orbit around the earth what is the most fuel efficient method of escaping
a satellite already in the earths heliocentric orbit can fire its engines only once what is the most fuel efficient
a satellite is lsquoparked in a circular orbit 250 km above the earths surface what is the most fuel efficient method
a satellite of mass m moves under the attractive inverse square field -mgamma r2r and is also subject to the linear
repeat the last problem for the case in which the particle moves under the simple harmonic attractive field -momega2rr
see the advance of the perihelion of mercury it is possible to lsquosee the advance of the perihelion of mercury
a non-linear oscillator satisfies the equation1 isinx2xmiddotmiddot x 0where isin is a small parameter use linstedts
a non-linear oscillator satisfies the equationxmiddotmiddot x isinx5 0where is a small parameter use linstedts
unsymmetrical oscillations a non-linear oscillator satisfies the equationxmiddotmiddot x x2 0where is a small
a limit cycle by perturbation theory use perturbation theory to investigate the limit cycle of rayleighs equation taken
phase paths in polar form show that the system of equationsxmiddot1 f1x1x2tnbspnbspnbspnbspnbsp xmiddot2
a dynamical system satisfies the equationsxmiddot x - y - x2 y2xymiddot x y - x2 y2yconvert this system into polar
a damped linear oscillator satisfies the equationxmiddotmiddot xmiddot x 0show that the polar equations for the
a particle of mass m can move on a rough horizontal table and is attached to a fixed point on the table by a light