The　dot　product　of　the　bases　vectors　on　the　super-surface　of　the　non-linear　non-holonomic　constraints　with　first　order,　expressed　by　quasi-coordinates　and　Mishirskii　equations　are　regarded　as　the　fundamental　equations　of　dynamics　with　non-linear　and　non-holonomic　constraints　in　first　order　for　the　system　of　the　variable　mass.　From　these　the　variant　differential　equations　of　dynamics　expressed　by　quasi-coordinates　were　derived.　The　fundamental　equations　of　dynamics　are　compatible　with　the　principle　of　Jourdain.