The Hudson River jibe is a very old time way of jibing in the days when boats had unstayed
rigs and sailed in the light summer winds of the Hudson Valley. It involves heading up slightly to increase boat speed and then throwing the helm over hard. In small boats it involved holding out the boom on the original tack until the last possible moment. If the boat is swung fast enough the boat is up towards a beam reach before the boom can swing across and fetch up on the sheets.
Now I must point out that a poorly performed Hudson River Jibe imparts enormous loads into the mainsheet attachment points, loads that can be sufficient to damage a boom or tear the mounting points out of the deck. The Hudson River cargo sloops that perfected the Hudson River jibe used what was called a ''Patent Horse''. The patent horse was the attachment point for the mainsheet blocks at the deck. The block was mounted on what was effectively a short traveller with huge springs on either side that kept the traveller car centered and which absorbed the tremendous shock of a jibe. The horse was rivetted or bolted to a huge transverse deck beam that was knee''d to a massive frame. It kind of gives you pause to think about getting the timing wrong on a boat with as big a mainsail and light an attachment point as the Nonsuch, if you see what I mean.
Jeff