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a bicycle chain consists of n freely jointed links forming a closed loop the chain can slide freely on a smooth
triangular coffee table a trendy swedish coffee table has an unsymmetrical triangular glass top supported by a leg at
leaning triangular panel a rough floor lies in the horizontal plane z 0 and the planes x 0 y 0 are occupied by
supermarket belt a circular cylinder which is axially symmetric but not uniform has mass m and moment of inertia mk2
yo-yo with moving support a uniform circular cylinder a yo-yo has a light inextensible string wrapped around it so that
a circular disk of mass m and radius a is smoothly pivoted about its axis of symmetry which is fixed in a horizontal
rolling or sliding a uniform ball is released from rest on a rough plane inclined at angle alpha to the horizontalthe
from sliding to rolling a snooker ball is at rest on the table when it is projected forward with speed v and no angular
general rigid pendulum a rigid body of general shape has mass m and can rotate freely about a fixed horizontal axis the
bug running on a hoop a uniform circular hoop of mass m can slide freely on a smooth horizontal table and a bug of mass
in the theory of dynamical systems a point is said to be an asymptotically stable equilibrium point if it lsquoattracts
projectile using cartesian coordinates find the hamiltonian for a projectile of mass m moving under uniform gravity
a smooth wire has the form of the helix x a cos theta y a sin theta z btheta where theta is a real parameter and a b
a particle is constrained to move over a smooth fixed surface under no forces other than the force of constraint by
a heavy uniform rope of length 2a is draped symmetrically over a thin smooth horizontal peg the rope is then disturbed
a uniform heavy rope of length a is held at rest with its two ends close together and the rope hanging symmetrically
a heavy uniform rope of mass m and length 4a has one end connected to a fixed point on a smooth horizontal table by
consider the system shown in figure 912 for the special case in which the particles p q have masses 2m m respectively
given figure shows two blocks of masses m and m that slide on smooth planes inclined at angles alpha and beta to the
the internal gravitational potential energy of a system of masses is sometimes called the self energy of the system the
a uniform rod of length 2a has one end smoothly pivoted at a fixed point o the other end is connected to a fixed point
van der pols equation use poincare-bendixson to show that van der pols equationxmiddotmiddot isinxmiddotx2-1 x 0has
a driven non-linear oscillator satisfies the equationxmiddotmiddot isinxmiddot3 x cos ptwhere p are positive
linstedts method use computer assistance to implement lindstedts method for the equationxmiddotmiddotxisinx30obtain a
a uniform ball is rolling in a straight line down a rough plane inclined at an angle alpha to the horizontalassuming