A Treatise On Dynamics
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223 172. If the two particles are not initially projected in the same plane, we must find the velocity of the centre of inertia of the system, and, by reversing it on each body of the system, we shall obtain their velocities relative to the centre of inertia. These velocities will be in parallel direc- tions and such that mu = m'u', and the plane passing through them is the plane of the relative motion.
Hence it is seen that the actual motion consists of the motion in the plane, while the plane..., remaining parallel to itself, moves with the centre of inertia.
173. We can also obtain these results from the equations of motion.
For, if X, y, z be the co-ordinates of one particle, x , y, z' of the other, r the distance between them, and R the force of each on the other, the equations of motion are.
mx = — R , r my = — R - — ^ , mz = ~ R mx = R -, r m'y'-Ry-^ , m'z'-R'-' " r r [ence we obtain X —x' y - f -y z —z p ™ + ™' / — , — ■ R , , X — X y — y z — z and, integrating, we find that (y - y') {z - z') -(z- z) (y - y') = A, (z — /)(« — x) —{x — x) (i — z) = B, ix-a!) iy-y') -{y-y) {x-af) = G, A, B, and G being constants, and .-.
What to read after A Treatise On Dynamics?
You can find similar books in the "Read Also" column, or choose other free books by W H William Henry Besant to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
223 172. If the two particles are not initially projected in the same plane, we must find the velocity of the centre of inertia of the system, and, by reversing it on each body of the system, we shall obtain their velocities relative to the centre of inertia. These velocities will be in parallel direc- tions and such that mu = m'u', and the plane passing through them is the plane of the relative motion.
Hence it is seen that the actual motion consists of the motion in the plane, while the plane..., remaining parallel to itself, moves with the centre of inertia.
173. We can also obtain these results from the equations of motion.
For, if X, y, z be the co-ordinates of one particle, x , y, z' of the other, r the distance between them, and R the force of each on the other, the equations of motion are.
mx = — R , r my = — R - — ^ , mz = ~ R mx = R -, r m'y'-Ry-^ , m'z'-R'-' " r r [ence we obtain X —x' y - f -y z —z p ™ + ™' / — , — ■ R , , X — X y — y z — z and, integrating, we find that (y - y') {z - z') -(z- z) (y - y') = A, (z — /)(« — x) —{x — x) (i — z) = B, ix-a!) iy-y') -{y-y) {x-af) = G, A, B, and G being constants, and .-.
What to read after A Treatise On Dynamics?
You can find similar books in the "Read Also" column, or choose other free books by W H William Henry Besant to read onlineMoreLess
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