it could be your engine mounts are needing replaced
The Corolla could be shaking for many reasons. Start by checking the wheel bearings and brakes for wear. Then check the engine to see if it running rough, causing the shake.
No. Bucking, I would consider an engine performance issue and shaking would be suspension or steering issues.
A bad valve or plug.
Timing needs adjustment is the most likely cause.
your problem is yu have a broken motor mount that will make the car shake when you start it and step on it
go see a mechanic
if the engine light is blinking a misfire condition has been detected. check plugs and wires.l
Does it quit shaking when it warms up? What engine and year of Aerostar?
It could be the harmonic balancer. The rubber on it can deteriorate. If it runs better at higher RPMs, take a look underneath and look at it. The belt on it drives all the other units.
If the problem disappears when the shifter in placed in neutral it could be a transmission or engine mounts
most likely misfiring cylinder(s) and/or worn engine mounts.