Description of main muscles used for each exercise:
Jog
Quads, hamstrings, calves & side of shoulders
Big Forwards circles
Shoulders, traps, upper back, lats & upper chest
Big Reverse Arm circles
Shoulders, traps, upper back, lats & upper chest
Arm swings across & back
Shoulders, upper back & chest
Arm swings up & back
Lats, lower back, shoulders
High Knees
Hip flexors, glutes, quads, hamstrings, core muscles
Butt Kicks
Hamstrings, glutes, core muscles
Sidesteps
Hip abductors, glutes, quads & hamstrings
Carioca Steps
Groin, outer thighs, quads, hamstrings & glutes
Walking Lunges with Trunk Rotation
Abdominals, hip flexors, glutes, quads, & hamstrings
Walking lunges with overhead reach
Glutes, quads, hamstrings, shoulders & lats
You can use many more variations for the dynamic warm up.