Final answer:
The equation can be transformed using the Lorentz transformation equations to deal with dx/dt and dy/dt and take into account time dilation and length contraction effects. β represents the velocity of the particle in its local reference frame, and γ is the Lorentz factor. The Lorentz transformation equations for velocity can be used to express velocities in terms of dx/dt and dy/dt.
Step-by-step explanation:
The equation you provided can be transformed to deal with dx/dt and dy/dt by using the Lorentz transformation equations. The Lorentz transformation equations are used to relate the coordinates and time measurements between two inertial reference frames. They take into account the time dilation and length contraction effects of special relativity.
In the Lorentz transformation equations, γ represents the Lorentz factor and is given by γ = 1/√(1 - β²), where β is the velocity of the particle as described by its local reference frame. So, γ is not equal to 1/√(1- β²); it is actually the reciprocal of that.
If you want to transform the equation to deal with dx/dt and dy/dt, you can use the Lorentz transformation equations for velocity, which relate the velocities in one reference frame to the velocities in another reference frame. This will allow you to express the velocities in terms of dx/dt and dy/dt.