Why are players stuttering?

Basically, I've got a model that moves with players moving along with that model. If the player look at their own character on their screen, they're not stuttering in any way, however, if they look at a different player on their screen, they appear to stutter/judder, even though the different player themselves doesn't. I've got this script currently but it is a local script which may be causing this, so I need a server version of this script so what do I need to change?

while true do

	local Players = game:GetService("Players")
	local player = game.Players.LocalPlayer
	local RunService = game:GetService('RunService')

	local LastHit
	local LastTrainCFrame

	local Function
	local Function2


	local Whitelist = {workspace:WaitForChild('Map1', 20)}
	
	
	Function = RunService.Heartbeat:Connect(function()
		local RootPart = player.Character.HumanoidRootPart
		local Ignore = player.Character
		local ray = Ray.new(RootPart.CFrame.p, Vector3.new(0,-200,0))
		local Hit, Position, Normal, Material
		if LastHit then
			Hit, Position, Normal, Material = workspace:FindPartOnRayWithWhitelist(ray,{LastHit})
			if not Hit then
				Hit, Position, Normal, Material = workspace:FindPartOnRayWithWhitelist(ray,Whitelist)
			end
		else
			Hit, Position, Normal, Material = workspace:FindPartOnRayWithWhitelist(ray,Whitelist)
		end
		if Hit then
			local Train = Hit
			if not LastTrainCFrame then
				LastTrainCFrame = Train.CFrame
			end
			local TrainCF
			if Train ~= LastHit and LastHit then
				TrainCF = LastHit.CFrame
			else
				TrainCF = Train.CFrame
			end
			local Rel = TrainCF * LastTrainCFrame:inverse()
			LastTrainCFrame = Train.CFrame
			RootPart.CFrame = Rel * RootPart.CFrame
			LastHit = Train
			if Train ~= LastHit then
				LastTrainCFrame = Train.CFrame
			end
		else
			LastTrainCFrame = nil
		end
		

		if not Function2 then
			Function2 = player.Character.Humanoid.Died:Connect(function()
				Function:Disconnect()
				Function2:Disconnect()

			end)
		end
	end)
	wait(140)
end