Q:

Near-future weapons taking designs similar to 17th century weapons

I am doing an alternate-history of Earth going into the science-fiction area. The split came with a portal to a new planet appearing around the 17th century. The portal deposited those brave enough to venture into it on the only continent on a new planet, roughly the size of the moon, with 25% earth gravity, and similar atmospheric makeup and atmospheric pressure.
The nation is having a technological revolution, putting them ahead of current-Earth, but tensions are also rising. What are some weapons derived from the 17th-century ones, that would fit a near-future setting? 

A:

If your 17th century cast-aways departed this realm before the Isaac Newton published his seminal works, then they could have developed their science on very different ideas.
A low-g world, recoil of firearms would be a more significant problem.  The moment of inertia of the human form firing a weapon lets us sight down our extended arms.  In a low-g environment, we’d either have to lower the weapon from our shoulder height or significantly widen our stance to maintain stability.  One choice reduces accuracy, and the other is uncomfortable — standing upright with ones legs maybe twice shoulder width (as an extreme example for illustration purposes).  So we might have developed rocketry into their weapons.  The lower gravity means the ballistic arc is flatter and would be easier to judge by eye.  Plus no recoil. 
And without Isaac Newton poisoning their minds, they’d still embraced the Aristotelean model when they left.  This would have given them warped understandings of the universe, and may be led them to surprising developments.
For instance, they still would have thought that the mechanical notion of impetus was a real thing.  In searching to understand it,  they might have unlocked deeper secrets of fundamental universal forces.  They might have cross bows that fired pure force bolts — no mass so no recoil.  
And, personal swords like foils and epee, being manifestations of honor and adulthood are still preferred.  But, they might be electrified or incorporate atomic force vibrations, or both, letting them slice through metal or deliver lethal discharges.  
The steel cuirasses worn by men-at-arms might be composed of pure force — to protect them against vibro-foils and vibro-epee — and can now stand up to modern non-alternate world rifle fire, because they never believed in those pesky Newton’s Laws of Motion.

