Traveling pieces are committed to their journey, and you can't give them any other orders while they are in transit, but even so, they can give check. This is because check and checkmate are pictorial in this game -- a Re1 gives check to a Ke8 if there are no intervening pieces, even though it can't really go to e8 and capture the enemy K (well, at least it can't go there all at once!) -- and likewise a traveling Rook at a4 would give check to an enemy K on h4, even though the R is going to be on a5 next turn. In fact, a R on a4 bound for a8 effectively gives check on both the 4th rank and the 5th rank because "if you are in check, but it is your opponent's turn to move, you have lost the game" (a common way of stating this rule).
Traveling pieces are committed to their journey, and if a piece gets in the way of a traveling piece nothing happens. Nothing happens, that is, except that you wind up having two pieces on the same square! And just because you have a Rook bound for a8, there's no reason you can't move another piece there! If they both arrive at the same time, they are both on the same square.
Traveling pieces cannot be stopped, and they cannot be captured.
When a crowd capture is made, all enemy pieces that are not traveling are removed and all friendly pieces are untouched.
Every move you make must be legal according to the position you see on the board, but interpreting the position in terms of normal Chess. (There are other variants that use "pictorial checkmate", and they also require you to interpret the board according to different sets of rules at the same time.) In particular, you should notice that a traveling piece may be in your way and block you from making a longer move.
Traveling Knights move Rookwise then diagonally . A Pawn's double step takes two moves to complete, and Castling also takes two moves to finish.
En passant capture is ... amusing! You can't capture the P while it's traveling, so you have to wait until it reaches its destination before capturing it as though it were on its previous square!
If you are not in check but have no legal moves, but some of your pieces are traveling, you must pass -- make a null move -- but if you have a legal move you must make it (you can't pass at will).
I think that covers all the necessary rules, at least for normal play. When this game is combined with other variants, some interesting questions arise.
For example, Progressive Lene Hau Chess: should a traveling piece advance once for a player's turn, or once for each move in that turn? I vote once per turn.
In addition, note that 1 Rg1xg7 g7-g5 saves the pawn from capture; the Rook still continues its journey to g7; or 1 Rg1xg7 h7-h5 tries to stop the Q from joining in, but 2 Qh2xh5 to be followed by 5 Qh5-h7 is the same length as the original Qh2-h7!
It could be worthwhile to make a shorter move: 1. Rg1-g4 for example, and (for example) Bc8-g4 would arrive too late to capture the Rook.
However, the thematic idea of this game is to launch long-range moves, one after another, all to arrive in the same area at the same time with an overwhelming attcke against a target that has had several moves in which to run away or change its shape or otherwise defend itself. A long move such as Rg1-g7 requires you to calculate more than seven moves ahead, simply because that's how long it takes the R to get there! The reward of deep calculation and long moves is that you have several pieces moving at the same time, which multiplies your force.
In classical Momentum Chess, if you play Rh1-h3, then on the next turn if the squares h4 and h5 are both empty the R will continue moving to h5, unless you use your move to stop it; and if it ever runs into another piece of either color, or if it eventually reaches h7 (on an 8x8 board, of course; it can go further on a 16x16 board, it will stop of its own accord; or if you plar Rh1-h2, it will continue to move forwards one square per turn, much like a traveling piece in Lene Hau Chess; the difference is that a "continuing" piece can be captured, can be stopped by running into another piece, or can be stopped by using your turn to order it to stop.
If you combine two rules in "Lene Hau Momentum Chess", then when you play 1. Rh1-h3, on move 2 the R is traveling, on move 3 it is continuing (at a speed of 2, to h5) and will stop if h4 or h5 are occupied, on move 4 it is traveling (and can move onto h5 even if it is occupied) -- it is a traveling-continuing piece! In the unplayably insane fantasy variant "Falling Off Lene Hau Momentum Chess", pieces can be in any of 5 conditions: standing, continuing, traveling, careening, or traveling-continuing! Although I will not try to resolve all the contradictions in the rules of the 3 games, I will say that you want to use functional checkmate so that you can have a Careening King.
Traveling pieces are under control, even though you cannot issue new orders to them until they arrive at journey's end -- and they will arrive, for nothing can stop them. The theme of Lene Hau Chess is controlling multiple pieces that are moving at the same time, and I believe that I can safely declare the game to be good, interesting, and playable without the need of extensive playtesting.
"Careening" is a rarely used word that is almost always followed by the phrase "out of control". Careening pieces can be diverted by the enemy, or can be brought back under control, but otherwise they will rush headlong to their doom. The theme of Falling Off is putting your opponent's pieces out of control, and I can't be sure its rules are perfect without playtesting.
Both games appear to be value-preserving, and so you should play them with Different Armies.
Both games required a lot of words to explain the rules, even though the basic concept was fairly simple and straightforward.
 That assertion should be checked by posting to alt.usage.english, where they live for such phrasemongering.