If we want to do a 0 degree launch so exact equatorial launch we can take the barge to the equator and launch from there we might save some fuel or 2 manoeuvres would be required one launch and one in orbit so this could be a big advantage plus polar launches can be done from anywhere also on thing I forgot to mention last time the SSPO orbit is a bit retrograde it's a little against the rotation so hovers around 98 deg. We can achive that too and suppose.

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if ISRO wants to do a secret launch for the miliatry and they don't want to reveal usually if you want to launch in civilian airspace or conduct a missile test you have to issue a NOTAM meaning Notice To Airmen so these hazard zones declare that a plane cant fly here or has to be safe so we can know if a missile test is about to happen so if a missile/rocket test/launch is happening in this area or not is ISRO wants to conduct a secret launch so they could take their rocket on barge to a area where planes dont fly or fly less and test it there without a potential NOTAM this could be an advantage but ISRO doesn't need that let's learn what other countries are doing. 

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So the complications for the barge are reduced so the barge doesn't have to handle the fuel if we put PSLV on a barge most stages are solid except the 4th stage which can be pre-fuelled because it uses earth storable propellant only issue is PSLV is huge more than 40m tall and the more your weight comes above the machine so your center of gravity will also come up so the instability will increase this could be a big issue 2nd issue is air conditioning for the spacecraft has to be arrnaged so basically the launchpad umbilicals many tubes also connect they keep the spacecraft and electronics cool so energy generation onboard will be required and this is for the PSLV only.

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if i talk about china's long march 11 is about 58 tonnes for refrence our AGNI V ICBm its 50 tonnes so LM11 is a very small rocket and a fully loaded PSLV weight for the XL variant with 6 strapon booster is 320 tonnes so a barge doesnt make sense will be a difficult task this will require a different system lets not even talk about the GSLV because it will require cryogenic fuel and what no keeping the tanks cold it's a big issue.