Playing long tones connects you to the universe.
Before you dismiss the above statement as "woo" (which it most certainly is), let's examine why I would start this post which such a claim.
Back in 2003, the New York Times ran this article which left a lasting impression on me. Supposedly there is a black hole in the Perseus galaxy cluster playing "the lowest note in the universe", a B flat 57 octaves lower than middle C. However, we can't hear this note because the time between oscillations is 10 million years (as compared to the one-twentieth of a second period at the bottom of our audible range). But trust them, it's there.
Here's where the "woo" comes in. Since our trumpets our pitched in B flat on the lowest open harmonic, we can connect to that cosmic frequency during our warmup.
Not buying it? Then forget all that and we'll get right to the step by step instructions.
Warm up with a drone.
No, not that BB-8 you bought at Radio Shack for your "kids" last Christmas. I'm speaking of a musical drone that will generate a static sustained pitch for you to play off. My drone of choice is the myNoise Indian Drone Tone in A# (Bb) available on Spotify but there are plenty of other options. Pick one that suits you.
Perhaps this one:
Now that you're all set up, let's play some long tones.
Pick an exercise (like the Arban's First Studies pictured above), get your B flat drone droning, and breathe deeply. Think of your warm up as a meditation, connecting your ear to your breath, to your voice, and to your horn.
Hear the B flat and sing it in any octave, feeling how it resonates in your body. Don't rush. Listen and tune it perfectly.
Buzz the low B flat on your mouthpiece. Again, feel how it resonates and tune it to where it sounds "perfect." Then slowly buzz the notes in your exercise freely (no metronome), tuning as you go. Take your time.
Replace your mouthpiece and slowly play the exercise freely on your horn. Again, feel that resonance and tune each note just right. Notice the similarities between each step. Notice the differences. Be aware.
Continue on with different exercises following all three steps. Do this for 10 minutes. Then take a break, breathe deeply, and relax.
Easy, right? Let me know how it works for you. Its definitely helped me.